## VAR-GARCH-M

Discussions of ARCH, GARCH, and related models

### VAR-GARCH-M

Hi,

I am using a bivariate garch in mean model to examine the effect of oil price uncertainty on real stock returns. I am using monthly data for real oil prices and real stock returns for the period 1973:1 - 2009:12.

The results show a positive effect of oil price uncertainty on stock returns (weird results), and I wonder whether I have errors in the code!
Last edited by economics2012 on Wed May 02, 2012 12:38 pm, edited 3 times in total.
economics2012

Posts: 62
Joined: Thu Jan 19, 2012 5:41 pm

### Re: VAR-GARCH-M

You'll probably need to provide more details if you want anyone to be able to help. For example, can you post the complete estimation results, along with a description of what the various variables are (unless it is completely obvious from the variable names)? You may also want to post the data set so others can try to repeat the estimation.

Also, can we assume that you've tested the OLS residuals for GARCH effects?

Thanks,
Tom Maycock
Estima
moderator

Posts: 306
Joined: Thu Oct 19, 2006 4:33 pm

### Re: VAR-GARCH-M

Hi Tom,

Here are my complete estimation results.

The variables used are: oilgrow which stand for: real oil price growth , and stock returns.

Code: Select all
`VAR/System - Estimation by Least SquaresMonthly Data From 1974:01 To 2009:12Usable Observations                       432Dependent Variable OILGROWMean of Dependent Variable       0.2369802905Std Error of Dependent Variable  7.0912551842Standard Error of Estimate       6.1203682923Sum of Squared Residuals         15245.775570Durbin-Watson Statistic                1.9786    Variable                        Coeff      Std Error      T-Stat      Signif************************************************************************************1.  OILGROW{1}                    0.520215612  0.049304475     10.55108  0.000000002.  OILGROW{2}                   -0.056023448  0.055598300     -1.00765  0.314222743.  OILGROW{3}                   -0.047396997  0.055730447     -0.85047  0.395564644.  OILGROW{4}                   -0.012540444  0.055509720     -0.22591  0.821381425.  OILGROW{5}                   -0.013774081  0.055804895     -0.24683  0.805167596.  OILGROW{6}                   -0.156653647  0.056013501     -2.79671  0.005407387.  OILGROW{7}                    0.076372676  0.056348410      1.35537  0.176052908.  OILGROW{8}                   -0.007260344  0.056523610     -0.12845  0.897857919.  OILGROW{9}                   -0.013793027  0.056821586     -0.24274  0.8083269910. OILGROW{10}                   0.034771912  0.057106989      0.60889  0.5429366111. OILGROW{11}                   0.077203440  0.057275340      1.34794  0.1784290212. OILGROW{12}                  -0.110411073  0.050948530     -2.16711  0.0308058513. STOCKRETURNS{1}               0.071504797  0.063697545      1.12257  0.2622829814. STOCKRETURNS{2}               0.009777206  0.063760930      0.15334  0.8782048615. STOCKRETURNS{3}               0.174765054  0.063528975      2.75095  0.0062075716. STOCKRETURNS{4}              -0.079545208  0.064202272     -1.23898  0.2160676517. STOCKRETURNS{5}               0.019224822  0.063627290      0.30215  0.7626940218. STOCKRETURNS{6}              -0.031107333  0.063744588     -0.48800  0.6258129119. STOCKRETURNS{7}              -0.017301692  0.063611910     -0.27199  0.7857689720. STOCKRETURNS{8}               0.006381151  0.063626547      0.10029  0.9201629221. STOCKRETURNS{9}               0.022956458  0.063569084      0.36113  0.7181925322. STOCKRETURNS{10}              0.031585505  0.063681602      0.49599  0.6201684523. STOCKRETURNS{11}             -0.008874725  0.063669535     -0.13939  0.8892130524. STOCKRETURNS{12}             -0.054992978  0.063458035     -0.86660  0.3866696925. Constant                      0.163708463  0.296075836      0.55293  0.5806166426. SQRTHOIL                      0.000000000  0.000000000      0.00000  0.00000000    F-Tests, Dependent Variable OILGROW              Variable           F-Statistic     Signif    *******************************************************    OILGROW                           13.3676    0.0000000    STOCKRETURNS                       0.9399    0.5066601Dependent Variable STOCKRETURNSMean of Dependent Variable       0.0211076390Std Error of Dependent Variable  4.8051892243Standard Error of Estimate       4.7505842819Sum of Squared Residuals         9185.1967649Durbin-Watson Statistic                1.9954    Variable                        Coeff      Std Error      T-Stat      Signif************************************************************************************1.  OILGROW{1}                   -0.062631622  0.038269767     -1.63658  0.102490762.  OILGROW{2}                    0.081653285  0.043154986      1.89209  0.059187993.  OILGROW{3}                    0.004278068  0.043257558      0.09890  0.921268274.  OILGROW{4}                   -0.071395226  0.043086231     -1.65703  0.098283795.  OILGROW{5}                    0.016035537  0.043315344      0.37020  0.711422676.  OILGROW{6}                   -0.025565076  0.043477262     -0.58801  0.556851537.  OILGROW{7}                    0.000388776  0.043737216      0.00889  0.992912128.  OILGROW{8}                   -0.087855469  0.043873205     -2.00249  0.045895419.  OILGROW{9}                    0.045515656  0.044104491      1.03200  0.3026868610. OILGROW{10}                  -0.073375723  0.044326019     -1.65536  0.0986213811. OILGROW{11}                  -0.003679140  0.044456693     -0.08276  0.9340847712. OILGROW{12}                  -0.056065357  0.039545870     -1.41773  0.1570348013. STOCKRETURNS{1}               0.111850757  0.049441560      2.26228  0.0242065614. STOCKRETURNS{2}              -0.069348343  0.049490759     -1.40124  0.1619048915. STOCKRETURNS{3}               0.031606247  0.049310717      0.64096  0.5219087516. STOCKRETURNS{4}              -0.003463371  0.049833325     -0.06950  0.9446264817. STOCKRETURNS{5}               0.047549704  0.049387029      0.96280  0.3362208718. STOCKRETURNS{6}              -0.064160867  0.049478074     -1.29675  0.1954506919. STOCKRETURNS{7}               0.023529918  0.049375091      0.47655  0.6339351920. STOCKRETURNS{8}              -0.014721206  0.049386452     -0.29808  0.7657927821. STOCKRETURNS{9}              -0.032231345  0.049341850     -0.65323  0.5139798722. STOCKRETURNS{10}              0.047474881  0.049429185      0.96046  0.3373927123. STOCKRETURNS{11}             -0.020479281  0.049419819     -0.41439  0.6788038324. STOCKRETURNS{12}              0.044874198  0.049255654      0.91105  0.3628100625. Constant                      0.066856129  0.229811858      0.29092  0.7712631526. SQRTHOIL                      0.000000000  0.000000000      0.00000  0.00000000    F-Tests, Dependent Variable STOCKRETURNS              Variable           F-Statistic     Signif    *******************************************************    OILGROW                            1.7123    0.0617950    STOCKRETURNS                       0.8971    0.5499893Simplex Optimization, Trial 0. Function Calls: 60Old Function = -2778.401291     New Function = -2777.386240New Coefficients:      0.000000       0.520216      -0.056023      -0.047397      -0.012540     -0.013774      -0.156654       0.076373      -0.007260      -0.013793      0.034772       0.077203      -0.110411       0.071505       0.009777      0.157289      -0.079545       0.019225      -0.031107      -0.017302      0.006381       0.022956       0.031586      -0.008875      -0.054993      0.163708       0.000000      -0.062632       0.081653       0.004278     -0.071395       0.016036      -0.025565       0.000389      -0.087855      0.045516      -0.073376      -0.003679      -0.056065       0.111851     -0.069348       0.031606      -0.003463       0.047550      -0.064161      0.023530      -0.014721      -0.032231       0.047475      -0.020479      0.044874       0.066856       0.000000       7.058229       0.200000      0.600000       4.252406       0.200000       0.600000Simplex Optimization, Trial 1. Function Calls: 62Old Function = -2777.386240     New Function = -2735.504304New Coefficients:      0.000508       0.517570      -0.055739      -0.047156      -0.012477     -0.013704      -0.155857       0.075984      -0.007223      -0.013723      0.034595       0.076811      -0.109850       0.071141       0.009727      0.173876      -0.079141       0.019127      -0.030949      -0.017214      0.006349       0.022840       0.031425      -0.008830      -0.054713      0.162876       0.000508      -0.062313       0.081238       0.004256     -0.071032       0.015954      -0.025435       0.000387      -0.087409      0.045284      -0.073003      -0.003660      -0.055780       0.111282     -0.068996       0.031446      -0.003446       0.047308      -0.063835      0.023410      -0.014646      -0.032067       0.047233      -0.020375      0.044646       0.066516       0.000508       8.469875       0.198983      0.596949       4.230784       0.198983       0.596949Simplex Optimization, Trial 16. Function Calls: 137Old Function = -2735.504304     New Function = -2704.644081New Coefficients:      0.000000       0.520216      -0.056023      -0.047397      -0.012540     -0.013774      -0.156654       0.076373      -0.007260      -0.013793      0.034772       0.077203      -0.110411       0.071505       0.009777      0.174765      -0.079545       0.019225      -0.031107      -0.017302      0.006381       0.022956       0.031586      -0.008875      -0.054993      0.163708       0.000000      -0.062632       0.081653       0.004278     -0.071395       0.016036      -0.025565       0.000389      -0.087855      0.045516      -0.073376      -0.003679      -0.056065       0.111851     -0.069348       0.031606      -0.003463       0.047550      -0.064161      0.023530      -0.014721      -0.032231       0.047475      -0.020479      0.044874       0.066856       0.010000       9.881521       0.200000      0.600000       4.252406       0.200000       0.600000Simplex Optimization, Trial 32. Function Calls: 213Old Function = -2704.644081     New Function = -2683.913998New Coefficients:      0.000508       0.517570      -0.055739      -0.047156      -0.012477     -0.013704      -0.155857       0.075984      -0.007223      -0.013723      0.034595       0.076811      -0.109850       0.071141       0.009727      0.173876      -0.079141       0.019127      -0.030949      -0.017214      0.006349       0.022840       0.031425      -0.008830      -0.054713      0.162876       0.000508      -0.062313       0.081238       0.004256     -0.071032       0.015954      -0.025435       0.000387      -0.087409      0.045284      -0.073003      -0.003660      -0.055780       0.111282     -0.068996       0.031446      -0.003446       0.047308      -0.063835      0.023410      -0.014646      -0.032067       0.047233      -0.020375      0.044646       0.066516       0.000508      11.293167       0.198983      0.596949       4.230784       0.198983       0.596949Simplex Optimization, Trial 577. Function Calls: 1819Old Function = -2610.909923     New Function = -2608.539051New Coefficients:      0.002574       0.509967      -0.054616      -0.047515      -0.012541     -0.013641      -0.155869       0.078931      -0.006997      -0.013490      0.031247       0.075883      -0.123796       0.069329       0.009509      0.142970      -0.078219       0.019927      -0.027683      -0.016070      0.006350       0.022800       0.031360      -0.009205      -0.008627      0.169289      -0.003568      -0.063623       0.079332       0.004336     -0.068768       0.016136      -0.026307       0.000382      -0.084914      0.044794      -0.073696      -0.003742      -0.054623       0.106221     -0.066982       0.031509      -0.003578       0.046036      -0.065307      0.023652      -0.015249      -0.032593       0.047764      -0.020895      0.044653       0.066156       0.011425      14.862771       0.785629      0.301812       4.130916       0.196437       0.657537Non-Linear Optimization, Iteration 1. Function Calls 1893. Cosine of Angle between Direction and Gradient  0.6036428. Alpha used was 0.000000 Adjusted squared norm of gradient 19.30759 Diagnostic measure (0=perfect) 0.0000 Subiterations 1. Distance scale  1.000000000Old Function = -2608.539051     New Function = -2599.349002New Coefficients:      0.055356       0.507335      -0.056781      -0.050454      -0.007777     -0.011781      -0.155780       0.084212      -0.020437      -0.041736      0.027890       0.068036      -0.117581       0.041246      -0.014164      0.105471      -0.086404       0.018226      -0.019992       0.011165      0.015916       0.037352      -0.034349      -0.024337       0.027013      0.332242       0.000000      -0.094167       0.045066       0.008161     -0.050047       0.029877      -0.035787       0.013769      -0.072354      0.035727      -0.075542      -0.007173      -0.031695       0.088860     -0.020880       0.013768      -0.038687       0.033296      -0.067836      0.015371      -0.029024      -0.036324       0.041881      -0.008040      0.015062       0.060676       0.027382      14.945463       0.819208      0.000000       4.108014       0.169310       0.655544Non-Linear Optimization, Iteration 2. Function Calls 1954. Cosine of Angle between Direction and Gradient  0.2010777. Alpha used was 0.000000 Adjusted squared norm of gradient 8.660941 Diagnostic measure (0=perfect) 0.0000 Subiterations 1. Distance scale  1.000000000Old Function = -2599.349002     New Function = -2596.634363New Coefficients:      0.074416       0.501488      -0.067600      -0.061792      -0.007641     -0.010216      -0.153992       0.103579      -0.014355      -0.059174      0.021676       0.048216      -0.112987       0.021575      -0.028925      0.080070      -0.097519       0.024511      -0.008702       0.016514      0.016357       0.036656      -0.039998      -0.015240       0.043004      0.352439       0.000000      -0.046618       0.057530       0.024202     -0.046646       0.026829      -0.055762       0.021026      -0.064462      0.032103      -0.057572       0.002259      -0.008807       0.060172     -0.019467       0.012204      -0.042978       0.041637      -0.058994      0.017351      -0.027583      -0.040515       0.033590      -0.006256     -0.006670       0.052338       0.045787      14.542781       0.857614      0.000000       4.111264       0.154819       0.655882Non-Linear Optimization, Iteration 3. Function Calls 2015. Cosine of Angle between Direction and Gradient  0.0780976. Alpha used was 0.000000 Adjusted squared norm of gradient 6.895031 Diagnostic measure (0=perfect) 0.0000 Subiterations 1. Distance scale  1.000000000Old Function = -2596.634363     New Function = -2594.167546New Coefficients:      0.083703       0.509456      -0.071877      -0.069334      -0.006062     -0.009672      -0.161064       0.105383      -0.012909      -0.070766      0.020302       0.035980      -0.107331       0.017244      -0.027163      0.071929      -0.104700       0.031984      -0.001025       0.011712      0.022082       0.035854      -0.026055      -0.010232       0.036253      0.300744       0.000000      -0.036466       0.043943       0.016455     -0.052065       0.033340      -0.058015       0.036193      -0.055850      0.026906      -0.052720      -0.013253      -0.025869       0.073019     -0.020417       0.032967      -0.031669       0.043272      -0.059409      0.021111      -0.018681      -0.041689       0.034904      -0.005521     -0.007006      -0.018426       0.050201      13.868919       0.891285      0.000000       4.156036       0.157391       0.659005Non-Linear Optimization, Iteration 27. Function Calls 3485. Cosine of Angle between Direction and Gradient  0.1037753. Alpha used was 0.000000 Adjusted squared norm of gradient 0.1728131 Diagnostic measure (0=perfect) 0.7724 Subiterations 1. Distance scale  1.000000000Old Function = -2588.675250     New Function = -2588.623525New Coefficients:      0.095899       0.524238      -0.027220      -0.119051       0.027656     -0.017375      -0.155211       0.056500       0.022205      -0.085367      0.063674      -0.014771      -0.108334      -0.004291       0.011084      0.041451      -0.108275       0.040994       0.004199       0.023873      0.037537       0.020265      -0.055681      -0.005112       0.029246      0.228057       0.000000      -0.031989       0.023866       0.044970     -0.061442       0.038157      -0.064987       0.056494      -0.082748      0.032033      -0.037939       0.012323      -0.032148       0.087160     -0.012474       0.022819      -0.037020       0.041326      -0.055407      0.031656      -0.033960      -0.012982       0.043190      -0.015109     -0.011858      -0.256649       0.077899      11.156172       0.982766      0.000000       0.822560       0.129347       0.846681Non-Linear Optimization, Iteration 28. Function Calls 3546. Cosine of Angle between Direction and Gradient  0.1380861. Alpha used was 0.000000 Adjusted squared norm of gradient 0.03112548 Diagnostic measure (0=perfect) 0.4635 Subiterations 1. Distance scale  1.000000000Old Function = -2588.623525     New Function = -2588.606437New Coefficients:      0.096216       0.525013      -0.028507      -0.117273       0.026092     -0.017299      -0.154819       0.057367       0.021613      -0.084859      0.062868      -0.014193      -0.108342      -0.003726       0.010981      0.041400      -0.109128       0.041704       0.003784       0.024443      0.037761       0.020251      -0.055902      -0.005129       0.028963      0.230678       0.000000      -0.032645       0.024039       0.044853     -0.061384       0.038701      -0.065337       0.056465      -0.082263      0.031888      -0.037842       0.013421      -0.032111       0.087456     -0.012475       0.022429      -0.036202       0.041372      -0.055659      0.032305      -0.034142      -0.012703       0.042915      -0.015224     -0.012735      -0.266757       0.078550      11.152920       0.983035      0.000000       0.789128       0.129023       0.848427Non-Linear Optimization, Iteration 29. Function Calls 3607. Cosine of Angle between Direction and Gradient  0.1099209. Alpha used was 0.000000 Adjusted squared norm of gradient 0.01860308 Diagnostic measure (0=perfect) 0.2781 Subiterations 1. Distance scale  1.000000000Old Function = -2588.606437     New Function = -2588.593624New Coefficients:      0.096049       0.527689      -0.030678      -0.114108       0.024130     -0.017395      -0.153497       0.057169       0.022349      -0.084860      0.063444      -0.014105      -0.108920      -0.003474       0.010523      0.041069      -0.110081       0.043103       0.003158       0.025429      0.038678       0.019679      -0.056866      -0.004638       0.028775      0.232362       0.000000      -0.033464       0.024792       0.044498     -0.061396       0.039629      -0.065708       0.056220      -0.081343      0.031873      -0.038185       0.014704      -0.032278       0.087148     -0.012402       0.022267      -0.035258       0.041599      -0.055840      0.033048      -0.034354      -0.012268       0.042830      -0.015040     -0.013391      -0.284639       0.081450      11.127535       0.984034      0.000000       0.743873       0.128685       0.851075Non-Linear Optimization, Iteration 30. Function Calls 3668. Cosine of Angle between Direction and Gradient  0.1691721. Alpha used was 0.000000 Adjusted squared norm of gradient 0.01406628 Diagnostic measure (0=perfect) 0.1668 Subiterations 1. Distance scale  1.000000000Old Function = -2588.593624     New Function = -2588.588710New Coefficients:      0.096010       0.528449      -0.032010      -0.112945       0.023528     -0.017492      -0.152657       0.057021       0.023263      -0.085722      0.063686      -0.014062      -0.108955      -0.003283       0.010703      0.041631      -0.110629       0.043447       0.002855       0.025647      0.038392       0.019845      -0.056421      -0.004637       0.028683      0.233952       0.000000      -0.033783       0.025058       0.044110     -0.061423       0.039724      -0.065961       0.055941      -0.081099      0.031459      -0.038355       0.014862      -0.032396       0.087328     -0.012624       0.022412      -0.035569       0.041432      -0.056015      0.032973      -0.034338      -0.012509       0.042979      -0.015144     -0.013247      -0.289128       0.081189      11.131470       0.983780      0.000000       0.752197       0.128427       0.850742Non-Linear Optimization, Iteration 31. Function Calls 3729. Cosine of Angle between Direction and Gradient  0.1740419. Alpha used was 0.000000 Adjusted squared norm of gradient 0.008398739 Diagnostic measure (0=perfect) 0.1001 Subiterations 1. Distance scale  1.000000000Old Function = -2588.588710     New Function = -2588.584702New Coefficients:      0.095843       0.529501      -0.033363      -0.111246       0.022815     -0.017597      -0.151715       0.056354       0.024495      -0.086965      0.064606      -0.013881      -0.108822      -0.003212       0.010711      0.042046      -0.110873       0.043867       0.002312       0.025749      0.038222       0.020246      -0.056083      -0.004744       0.028726      0.235773       0.000000      -0.033591       0.025278       0.043948     -0.061458       0.039604      -0.065882       0.055786      -0.080990      0.031194      -0.038491       0.014734      -0.032652       0.087369     -0.012709       0.022672      -0.035685       0.041466      -0.055961      0.032803      -0.034368      -0.012727       0.043195      -0.014982     -0.012706      -0.289962       0.081976      11.141576       0.983306      0.000000       0.764931       0.128209       0.850256Non-Linear Optimization, Iteration 32. Function Calls 3790. Cosine of Angle between Direction and Gradient  0.1228157. Alpha used was 0.000000 Adjusted squared norm of gradient 0.003486388 Diagnostic measure (0=perfect) 0.0601 Subiterations 1. Distance scale  1.000000000Old Function = -2588.584702     New Function = -2588.583851New Coefficients:      0.095750       0.530206      -0.033756      -0.110685       0.022799     -0.017573      -0.151230       0.055522       0.025648      -0.087552      0.065456      -0.014301      -0.108872      -0.003584       0.010735      0.042100      -0.110536       0.043990       0.002258       0.025817      0.038255       0.019871      -0.056085      -0.004501       0.028762      0.235850       0.000000      -0.033460       0.025208       0.044047     -0.061549       0.039407      -0.065595       0.055766      -0.081332      0.031269      -0.038407       0.014493      -0.032639       0.087266     -0.012644       0.022623      -0.035901       0.041332      -0.055746      0.032668      -0.034296      -0.012808       0.043117      -0.015065     -0.012342      -0.292479       0.082289      11.135539       0.983340      0.000000       0.770127       0.128129       0.850151Non-Linear Optimization, Iteration 33. Function Calls 3851. Cosine of Angle between Direction and Gradient  0.1184611. Alpha used was 0.000000 Adjusted squared norm of gradient 0.0004671975 Diagnostic measure (0=perfect) 0.0360 Subiterations 1. Distance scale  1.000000000Old Function = -2588.583851     New Function = -2588.583619New Coefficients:      0.095826       0.530151      -0.033883      -0.110572       0.022753     -0.017493      -0.151313       0.055514       0.025637      -0.087601      0.065337      -0.014119      -0.108758      -0.003573       0.010716      0.042172      -0.110491       0.043963       0.002129       0.025775      0.038208       0.020024      -0.055973      -0.004673       0.028782      0.236169       0.000000      -0.033249       0.025064       0.044186     -0.061529       0.039295      -0.065472       0.055911      -0.081450      0.031364      -0.038281       0.014386      -0.032603       0.087311     -0.012619       0.022565      -0.035819       0.041412      -0.055660      0.032627      -0.034322      -0.012749       0.043077      -0.015036     -0.012407      -0.290088       0.082092      11.140185       0.983187      0.000000       0.766869       0.128094       0.850346Non-Linear Optimization, Iteration 34. Function Calls 3912. Cosine of Angle between Direction and Gradient  0.1295045. Alpha used was 0.000000 Adjusted squared norm of gradient 0.0001071594 Diagnostic measure (0=perfect) 0.0216 Subiterations 1. Distance scale  1.000000000Old Function = -2588.583619     New Function = -2588.583564New Coefficients:      0.095847       0.530103      -0.033819      -0.110586       0.022734     -0.017466      -0.151331       0.055482       0.025643      -0.087535      0.065272      -0.014108      -0.108736      -0.003564       0.010725      0.042102      -0.110448       0.043979       0.002112       0.025796      0.038202       0.019964      -0.055984      -0.004665       0.028764      0.236069       0.000000      -0.033226       0.024976       0.044243     -0.061504       0.039245      -0.065396       0.055947      -0.081540      0.031438      -0.038204       0.014369      -0.032538       0.087324     -0.012576       0.022512      -0.035798       0.041442      -0.055618      0.032658      -0.034323      -0.012682       0.043024      -0.015062     -0.012512      -0.289192       0.081928      11.138885       0.983160      0.000000       0.764623       0.128073       0.850462Non-Linear Optimization, Iteration 35. Function Calls 3973. Cosine of Angle between Direction and Gradient  0.0959132. Alpha used was 0.000000 Adjusted squared norm of gradient 4.232889e-005 Diagnostic measure (0=perfect) 0.0130 Subiterations 1. Distance scale  1.000000000Old Function = -2588.583564     New Function = -2588.583544New Coefficients:      0.095864       0.530113      -0.033825      -0.110561       0.022693     -0.017448      -0.151339       0.055465       0.025661      -0.087503      0.065245      -0.014117      -0.108761      -0.003561       0.010732      0.042088      -0.110441       0.043976       0.002121       0.025838      0.038231       0.019928      -0.055996      -0.004671       0.028759      0.236100       0.000000      -0.033215       0.024946       0.044270     -0.061476       0.039214      -0.065362       0.055961      -0.081561      0.031500      -0.038173       0.014319      -0.032504       0.087326     -0.012588       0.022479      -0.035800       0.041463      -0.055621      0.032657      -0.034323      -0.012644       0.043006      -0.015059     -0.012570      -0.288540       0.081781      11.137164       0.983179      0.000000       0.764080       0.128073       0.850494Non-Linear Optimization, Iteration 36. Function Calls 4034. Cosine of Angle between Direction and Gradient  0.0980764. Alpha used was 0.000000 Adjusted squared norm of gradient 2.070718e-005 Diagnostic measure (0=perfect) 0.0078 Subiterations 1. Distance scale  1.000000000Old Function = -2588.583544     New Function = -2588.583533New Coefficients:      0.095856       0.530123      -0.033825      -0.110521       0.022633     -0.017448      -0.151322       0.055453       0.025672      -0.087489      0.065246      -0.014128      -0.108789      -0.003547       0.010734      0.042058      -0.110454       0.043989       0.002130       0.025865      0.038240       0.019893      -0.056018      -0.004658       0.028759      0.236050       0.000000      -0.033218       0.024933       0.044257     -0.061454       0.039200      -0.065354       0.055944      -0.081571      0.031528      -0.038172       0.014302      -0.032478       0.087328     -0.012576       0.022483      -0.035799       0.041468      -0.055651      0.032656      -0.034317      -0.012618       0.043006      -0.015067     -0.012603      -0.287781       0.081664      11.135754       0.983196      0.000000       0.764295       0.128075       0.850481Non-Linear Optimization, Iteration 37. Function Calls 4095. Cosine of Angle between Direction and Gradient  0.1084149. Alpha used was 0.000000 Adjusted squared norm of gradient 1.173717e-005 Diagnostic measure (0=perfect) 0.0047 Subiterations 1. Distance scale  1.000000000Old Function = -2588.583533     New Function = -2588.583527New Coefficients:      0.095852       0.530133      -0.033823      -0.110486       0.022582     -0.017453      -0.151307       0.055455       0.025671      -0.087485      0.065266      -0.014140      -0.108806      -0.003537       0.010740      0.042044      -0.110464       0.044001       0.002150       0.025882      0.038252       0.019886      -0.056027      -0.004653       0.028765      0.236057       0.000000      -0.033228       0.024943       0.044249     -0.061438       0.039198      -0.065370       0.055926      -0.081551      0.031536      -0.038187       0.014295      -0.032481       0.087324     -0.012590       0.022478      -0.035796       0.041466      -0.055682      0.032646      -0.034328      -0.012615       0.043015      -0.015063     -0.012592      -0.287130       0.081571      11.134854       0.983211      0.000000       0.764711       0.128080       0.850456Non-Linear Optimization, Iteration 38. Function Calls 4156. Cosine of Angle between Direction and Gradient  0.1684459. Alpha used was 0.000000 Adjusted squared norm of gradient 3.899427e-006 Diagnostic measure (0=perfect) 0.0028 Subiterations 1. Distance scale  1.000000000Old Function = -2588.583527     New Function = -2588.583525New Coefficients:      0.095849       0.530129      -0.033826      -0.110474       0.022565     -0.017453      -0.151305       0.055461       0.025663      -0.087487      0.065281      -0.014153      -0.108805      -0.003539       0.010748      0.042043      -0.110463       0.043998       0.002159       0.025880      0.038250       0.019887      -0.056033      -0.004656       0.028771      0.236065       0.000000      -0.033225       0.024943       0.044240     -0.061441       0.039206      -0.065385       0.055924      -0.081548      0.031524      -0.038199       0.014305      -0.032488       0.087326     -0.012590       0.022489      -0.035790       0.041458      -0.055694      0.032640      -0.034328      -0.012626       0.043022      -0.015069     -0.012577      -0.286838       0.081541      11.134762       0.983218      0.000000       0.764857       0.128082       0.850447Non-Linear Optimization, Iteration 39. Function Calls 4217. Cosine of Angle between Direction and Gradient  0.2833513. Alpha used was 0.000000 Adjusted squared norm of gradient 8.387825e-007 Diagnostic measure (0=perfect) 0.0017 Subiterations 1. Distance scale  1.000000000Old Function = -2588.583525     New Function = -2588.583525New Coefficients:      0.095850       0.530128      -0.033821      -0.110473       0.022563     -0.017453      -0.151306       0.055462       0.025657      -0.087485      0.065292      -0.014163      -0.108796      -0.003543       0.010752      0.042042      -0.110455       0.043998       0.002164       0.025876      0.038248       0.019888      -0.056032      -0.004658       0.028772      0.236066       0.000000      -0.033225       0.024945       0.044244     -0.061445       0.039213      -0.065394       0.055928      -0.081543      0.031514      -0.038204       0.014316      -0.032498       0.087326     -0.012595       0.022485      -0.035789       0.041456      -0.055691      0.032639      -0.034336      -0.012638       0.043023      -0.015070     -0.012566      -0.286732       0.081527      11.134812       0.983218      0.000000       0.764829       0.128082       0.850449Non-Linear Optimization, Iteration 40. Function Calls 4278. Cosine of Angle between Direction and Gradient  0.2353028. Alpha used was 0.000000 Adjusted squared norm of gradient 2.31118e-007 Diagnostic measure (0=perfect) 0.0010 Subiterations 1. Distance scale  1.000000000Old Function = -2588.583525     New Function = -2588.583525New Coefficients:      0.095852       0.530126      -0.033822      -0.110474       0.022566     -0.017451      -0.151308       0.055462       0.025655      -0.087481      0.065294      -0.014168      -0.108791      -0.003545       0.010755      0.042041      -0.110451       0.043996       0.002166       0.025875      0.038246       0.019888      -0.056032      -0.004659       0.028772      0.236075       0.000000      -0.033224       0.024943       0.044246     -0.061448       0.039217      -0.065396       0.055933      -0.081545      0.031510      -0.038203       0.014321      -0.032502       0.087326     -0.012595       0.022485      -0.035789       0.041457      -0.055687      0.032641      -0.034337      -0.012642       0.043022      -0.015071     -0.012567      -0.286718       0.081524      11.134813       0.983218      0.000000       0.764773       0.128081       0.850452Non-Linear Optimization, Iteration 41. Function Calls 4339. Cosine of Angle between Direction and Gradient  0.3163347. Alpha used was 0.000000 Adjusted squared norm of gradient 4.465044e-008 Diagnostic measure (0=perfect) 0.0006 Subiterations 1. Distance scale  1.000000000Old Function = -2588.583525     New Function = -2588.583525New Coefficients:      0.095852       0.530128      -0.033822      -0.110474       0.022567     -0.017451      -0.151308       0.055461       0.025654      -0.087479      0.065294      -0.014169      -0.108790      -0.003546       0.010755      0.042041      -0.110450       0.043996       0.002165       0.025875      0.038245       0.019886      -0.056032      -0.004659       0.028771      0.236072       0.000000      -0.033223       0.024942       0.044248     -0.061449       0.039218      -0.065396       0.055935      -0.081547      0.031511      -0.038203       0.014322      -0.032502       0.087326     -0.012595       0.022484      -0.035790       0.041459      -0.055686      0.032642      -0.034338      -0.012642       0.043021      -0.015071     -0.012570      -0.286719       0.081523      11.134805       0.983218      0.000000       0.764757       0.128081       0.850453Non-Linear Optimization, Iteration 42. Function Calls 4400. Cosine of Angle between Direction and Gradient  0.1460616. Alpha used was 0.000000 Adjusted squared norm of gradient 9.944952e-009 Diagnostic measure (0=perfect) 0.0004 Subiterations 1. Distance scale  1.000000000Old Function = -2588.583525     New Function = -2588.583525New Coefficients:      0.095852       0.530128      -0.033823      -0.110474       0.022568     -0.017452      -0.151307       0.055461       0.025653      -0.087478      0.065294      -0.014170      -0.108789      -0.003546       0.010756      0.042041      -0.110450       0.043996       0.002165       0.025875      0.038246       0.019887      -0.056032      -0.004659       0.028771      0.236073       0.000000      -0.033223       0.024942       0.044248     -0.061449       0.039218      -0.065396       0.055936      -0.081547      0.031512      -0.038203       0.014323      -0.032503       0.087326     -0.012595       0.022484      -0.035791       0.041459      -0.055685      0.032643      -0.034338      -0.012642       0.043021      -0.015071     -0.012571      -0.286718       0.081523      11.134788       0.983218      0.000000       0.764757       0.128081       0.850453MAXIMIZE - Estimation by BFGSConvergence in    42 Iterations. Final criterion was  0.0000016 <=  0.0000100Monthly Data From 1974:01 To 2009:12Usable Observations                       432Function Value                     -2588.5835    Variable                        Coeff      Std Error      T-Stat      Signif************************************************************************************1.  B                              0.09585250   0.03127439      3.06489  0.002177522.  BVEC(1)(1)                     0.53012820   0.05028247     10.54300  0.000000003.  BVEC(1)(2)                    -0.03382281   0.03860605     -0.87610  0.380975094.  BVEC(1)(3)                    -0.11047403   0.04279874     -2.58124  0.009844475.  BVEC(1)(4)                     0.02256768   0.04294121      0.52555  0.599202076.  BVEC(1)(5)                    -0.01745154   0.02681079     -0.65091  0.515101467.  BVEC(1)(6)                    -0.15130741   0.03258400     -4.64361  0.000003428.  BVEC(1)(7)                     0.05546113   0.03518137      1.57643  0.114925649.  BVEC(1)(8)                     0.02565334   0.04283871      0.59884  0.5492825510. BVEC(1)(9)                    -0.08747772   0.03943955     -2.21802  0.0265534711. BVEC(1)(10)                    0.06529450   0.03946081      1.65467  0.0979920912. BVEC(1)(11)                   -0.01416972   0.03790634     -0.37381  0.7085467513. BVEC(1)(12)                   -0.10878948   0.02934713     -3.70699  0.0002097414. BVEC(1)(13)                   -0.00354579   0.03691264     -0.09606  0.9234736915. BVEC(1)(14)                    0.01075567   0.04309607      0.24957  0.8029165816. BVEC(1)(15)                    0.04204084   0.04085463      1.02903  0.3034633117. BVEC(1)(16)                   -0.11045016   0.03602444     -3.06598  0.0021695918. BVEC(1)(17)                    0.04399617   0.03620323      1.21526  0.2242687519. BVEC(1)(18)                    0.00216526   0.04073171      0.05316  0.9576051320. BVEC(1)(19)                    0.02587499   0.04265024      0.60668  0.5440641321. BVEC(1)(20)                    0.03824552   0.04041933      0.94622  0.3440370522. BVEC(1)(21)                    0.01988663   0.04163203      0.47768  0.6328807123. BVEC(1)(22)                   -0.05603180   0.04212411     -1.33016  0.1834656424. BVEC(1)(23)                   -0.00465893   0.03895077     -0.11961  0.9047914425. BVEC(1)(24)                    0.02877134   0.03609311      0.79714  0.4253684026. BVEC(1)(25)                    0.23607305   0.18802043      1.25557  0.2092714427. BVEC(1)(26)                    0.00000000   0.00000000      0.00000  0.0000000028. BVEC(2)(1)                    -0.03322330   0.03748393     -0.88633  0.3754372829. BVEC(2)(2)                     0.02494214   0.03483301      0.71605  0.4739612030. BVEC(2)(3)                     0.04424796   0.03268036      1.35396  0.1757485031. BVEC(2)(4)                    -0.06144929   0.03087430     -1.99031  0.0465573132. BVEC(2)(5)                     0.03921773   0.03170393      1.23700  0.2160874633. BVEC(2)(6)                    -0.06539563   0.02848592     -2.29572  0.0216920534. BVEC(2)(7)                     0.05593624   0.03049274      1.83441  0.0665929235. BVEC(2)(8)                    -0.08154739   0.03420693     -2.38394  0.0171282236. BVEC(2)(9)                     0.03151176   0.02892760      1.08933  0.2760074537. BVEC(2)(10)                   -0.03820279   0.03021077     -1.26454  0.2060354338. BVEC(2)(11)                    0.01432259   0.03342856      0.42845  0.6683208339. BVEC(2)(12)                   -0.03250296   0.03313018     -0.98107  0.3265593040. BVEC(2)(13)                    0.08732603   0.05644643      1.54706  0.1218487041. BVEC(2)(14)                   -0.01259509   0.05471921     -0.23018  0.8179544442. BVEC(2)(15)                    0.02248448   0.04855820      0.46304  0.6433342843. BVEC(2)(16)                   -0.03579113   0.04925730     -0.72662  0.4674613544. BVEC(2)(17)                    0.04145924   0.04796702      0.86433  0.3874077345. BVEC(2)(18)                   -0.05568539   0.04603051     -1.20975  0.2263750046. BVEC(2)(19)                    0.03264276   0.05147225      0.63418  0.5259622747. BVEC(2)(20)                   -0.03433788   0.04887338     -0.70259  0.4823121348. BVEC(2)(21)                   -0.01264198   0.03402305     -0.37157  0.7102123449. BVEC(2)(22)                    0.04302130   0.04149468      1.03679  0.2998334350. BVEC(2)(23)                   -0.01507078   0.04863744     -0.30986  0.7566676751. BVEC(2)(24)                   -0.01257103   0.04561292     -0.27560  0.7828534652. BVEC(2)(25)                   -0.28671814   0.40142566     -0.71425  0.4750728353. BVEC(2)(26)                    0.08152284   0.06178002      1.31957  0.1869798354. GARCHP(1)(1)                  11.13478778   1.41768408      7.85421  0.0000000055. GARCHP(1)(2)                   0.98321750   0.02284533     43.03800  0.0000000056. GARCHP(1)(3)                   0.00000000   0.00000000      0.00000  0.0000000057. GARCHP(2)(1)                   0.76475712   0.47982621      1.59382  0.1109761158. GARCHP(2)(2)                   0.12808063   0.01898348      6.74695  0.0000000059. GARCHP(2)(3)                   0.85045337   0.02957501     28.75581  0.00000000SIC for VAR    5632.52461SIC for GARCH-M    5523.06731`

I also attached the data file with three columns: date, oil growth and stock returns.

I believe line 53. of the last table shows the effect of oil price uncertainty on stock returns with a positive coefficient of 0.08152284 and t-statistics of 1.31957.

In regard of testing the OLS residuals for GARCH effects, I am not sure whether you meant what I got in the first table above!
Is there any RATS wizard for testing the OLS residuals for GARCH effects?

Thanks a lot,
Last edited by economics2012 on Wed May 30, 2012 1:03 pm, edited 1 time in total.
economics2012

Posts: 62
Joined: Thu Jan 19, 2012 5:41 pm

### Re: VAR-GARCH-M

Note that what you're estimating isn't a standard VAR-GARCH-M, but Elder's specialized version. The "weird" result is a positive but insignificant coefficient so you probably shouldn't be that concerned. BTW, you are including in your data set the 1970's when (U.S.) oil prices were controlled and the stock market was weak.
TomDoan

Posts: 2722
Joined: Wed Nov 01, 2006 5:36 pm

### Re: VAR-GARCH-M

Hi Tom,

Correct, I am following Elder's representation. I am examining oil price uncertainty on aggregate and sectoral level stock returns.

Results for automobile, retail and steel returns, for instance, show positive and significant results! I will attach the data set for some of the sectors.

What do you suggest in regards of the data?

thanks a lot
economics2012

Posts: 62
Joined: Thu Jan 19, 2012 5:41 pm

### Re: VAR-GARCH-M

Hi Tom,

Attached are the data sets for three different returns, the automobile, steel and retail.

Best,
Last edited by economics2012 on Wed May 30, 2012 1:04 pm, edited 1 time in total.
economics2012

Posts: 62
Joined: Thu Jan 19, 2012 5:41 pm

### Re: VAR-GARCH-M

A GARCH model doesn't describe the dynamics of the oil growth series very well. Instead of volatility clustering, you get about four really large spikes (two up, two down). Feed the generated standard deviation series into a regression and you have basically a dummy variable with four 1's and everything else 0's. That will be the same regardless of the other series that you use for stock returns. You're never going to get good statistical inference from a 4 data point dummy.
TomDoan

Posts: 2722
Joined: Wed Nov 01, 2006 5:36 pm

### Re: VAR-GARCH-M

So you mean the problem is in the real price of oil that I cannot estimate a GARCH model? Elder and Serletis(2010), in their paper "Oil Price Uncertainty", Journal of Money, Credit and Banking, Vol. 42, No. 6, 1137-1159, have used the oil price-GDP bivariate VAR-GARCH-M model. They used quarterly data while mine is monthly.
Last edited by economics2012 on Mon Feb 20, 2012 9:51 pm, edited 1 time in total.
economics2012

Posts: 62
Joined: Thu Jan 19, 2012 5:41 pm

### Re: VAR-GARCH-M

I'm not sure their GARCH model fit the oil price any better than yours did, but they are working with a target variable of quarterly GDP, which doesn't react as quickly as your stock price series. If the GARCH model doesn't fit oil prices well, then adding the predicted variance from a poorly-fitting model isn't likely to give useful information, plus much of the information from the past oil prices may already be priced in.

At any rate, the calculations are correct given your data.
TomDoan

Posts: 2722
Joined: Wed Nov 01, 2006 5:36 pm

### Re: VAR-GARCH-M

Thanks a lot Tom.
economics2012

Posts: 62
Joined: Thu Jan 19, 2012 5:41 pm

### Re: VAR-GARCH-M

Dear Tom,

I re-ran the GARCH model using daily data instead of monthly data. The results show POSITIVE and significant effect of oil price uncertainty on the Retail returns, and Entertainment returns. However, The results are supposed to be either negative or insignificant. For the aggregate returns and the other sectors, the results came out insignificant.

I attached below the data, code and results for the retail sector.

Last edited by economics2012 on Wed May 02, 2012 12:42 pm, edited 2 times in total.
economics2012

Posts: 62
Joined: Thu Jan 19, 2012 5:41 pm

### Re: VAR-GARCH-M

I need to check whether the mean in the above model is correctly specified or I still have GARCH effects using the daily data.

Any help is greatly appreciated,
economics2012

Posts: 62
Joined: Thu Jan 19, 2012 5:41 pm

### Re: VAR-GARCH-M

You copied a constraint which was specific to the original example which had GDP (which has no GARCH effect) as one of the variables. So you were knocking the GARCH term out of the stock market returns. If you take that out:

nonlin b bvec garchp bvec(1)(38)=0.0

you get a better fitting model. However, you still end up with a positive and (barely) significant coefficient on the oil price volatility. However, other than the error I just pointed out the model is set up correctly.
TomDoan

Posts: 2722
Joined: Wed Nov 01, 2006 5:36 pm

### Re: VAR-GARCH-M

So why "nonlin b bvec garchp bvec(1)(38)=0.0" is specific for GDP and not for stock returns?
economics2012

Posts: 62
Joined: Thu Jan 19, 2012 5:41 pm

### Re: VAR-GARCH-M

Sorry for the confusion. You copied the following out of the original example (with adjustment for the number of lags)

*
* In an unconstrained estimation, one of the GARCH coefficients goes
* negative. We peg it to zero. The model estimated in the paper also
* constrains the "M" term on the oil price in the oil (1st) equation to
* zero.
*
nonlin b bvec garchp garchp(1)(3)=0.0 bvec(1)(38)=0.0

The first constaint was specific to the Elder-Serletis example. When we estimated the model without it, that parameter went negative, so we re-estimated it constrained. Your data doesn't need it, so your nonlin should read

nonlin b bvec garchp bvec(1)(38)=0.0
TomDoan

Posts: 2722
Joined: Wed Nov 01, 2006 5:36 pm

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