This focuses on forecasting a single variable using time series methods, such as ARIMA (Box-Jenkins) modeling, exponential smoothing, and spectral methods. For a general introduction to basic forecasting concepts and the instructions used to produce forecasts, please see the Forecasting page. That also provides information on regression-based (y on exogenous x) forecasting models. For forecasting with more than one variable, see Vector Autoregressions or Simultaneous Equations. You can also use State Space Models for forecasting either one or several variables.

 

Time series modeling techniques forecast the future by

1.modeling the correlation between a series (or group of series) and its (their) past,

2.assuming that the relationship between current and past will continue into the future, and

3.computing forecasts on the basis of those assumptions.

They are extrapolative techniques which incorporate no information other than that available in the past data.

 

Methods

RATS supports three methods for univariate time series forecasting:

 

Exponential smoothing

is a small collection of models which are often adequate for forecasting. Unlike the other methods, it does not really attempt to model the autocorrelation. You choose a model based upon the two most important aspects of time series behavior: trend and seasonality.

 

Box-Jenkins/ARIMA Modeling

offers a broad collection of models for fitting the serial correlation pattern. Because of the number of choices permitted, it can handle many types of time series. Choosing an appropriate model, however, is something of an art.

 

Spectral forecasting

uses frequency domain techniques to fit a “generic” Box-Jenkins model. It produces very acceptable forecasts relative to Box-Jenkins models, but is less robust to errors in preparing the data for forecasts. It also requires more data than Box-Jenkins.

 

You can also forecast using state-space models, and do multivariate time series forecasting with vector autoregressive models. And you can produce forecasts using a variety of standard regression models.

 

In the remainder of this page, we’ll examine some issues that are common to all three of these modeling techniques. Each method has its own page with the links above.

 

Common Issues

There are several issues which all three of these time series methods must address, and which are examined in this section:

•Should you transform the data prior to the analysis? Usually this boils down to a question of logs vs levels.

•How should you represent the series trend? Should you difference the series?

•How should you treat seasonality?

•How many parameters can you safely estimate given the available data?

Preliminary Transformations

Preliminary transformations are simple transformations with two purposes: to straighten out trends; and to produce approximately uniform variability in the series over the sample range.

 

What we are trying to eliminate in the second point is a systematic tendency for the magnitude of the variance to depend upon the magnitude of the data. Suppose that the variance of a series is significantly higher when its values are large. If we estimate a model for this series by least squares, the least squares algorithm will concentrate upon fitting the high-variance part, largely ignoring the rest of the data.

 

Usually, you will either do nothing to the data, take square roots, or take logarithms. How do you decide? The following guidelines should help:

•Do you usually think of the series in terms of its growth rates (GNP, money, prices, etc.)? If so, take logs.

•Is the percent growth rate of the series an almost meaningless concept? Usually, do nothing. Possibly take the square root if the series clearly is more variable at higher values.

Typically, if your decision is not obvious from looking at the data, your choice will make little difference to the forecasts.

 

Differencing

We will look at this together with the decision of whether or not to include an intercept. This is a crucial decision for two reasons. First, some forecasting methods (especially spectral procedures) are computationally sensitive to mistakes here, particularly to underdifferencing. Second, this determines the trend behavior of the forecasts, so an incorrect choice will have major effects on longer-term forecasts. Modeling methodologies which do not include the correct trend model are likely to produce poor forecasts.

 

The table below suggests some differencing and intercept combinations for various types of series behavior. Often, you can decide how to difference solely on the basis of your knowledge of the data.

 

 

Seasonality

Seasonality poses several serious problems for forecasters:

•It can take many forms: additive or multiplicative, stationary or non-stationary, stochastic or deterministic.

•Seasonality usually accounts for most of the variance of the series, making it difficult to determine the non-seasonal behavior.

•Every method of dealing with seasonality induces degrees of freedom problems. This will either cause a loss of usable data points, or require estimation of seasonal parameters with very few data points.

 

If seasonality is essential to the task at hand, you have two basic courses of action:

•You can seasonally adjust the data, forecast the adjusted data and the seasonal part separately, and then combine them. The main problem is that the seasonal “model” is done independently and may be inappropriate for the data series.

•You can use a methodology which incorporates seasonality directly. All three of the forecasting methods permit this. However, you will only be able to handle adequately certain forms of seasonality.

 

Parsimony

While the “Principle of Parsimony” is usually associated with Box and Jenkins, the idea applies to other forecasting models as well. Keep in mind two general principles:

•Don’t ask the data to do too much work. The less data you have, the fewer parameters you can estimate, and the more important your judgment becomes.

•Don’t take your model too seriously. Time series models are designed to fit the serial correlation properties of the data, not explain them. The goal is to find a model which fits the data reasonably well with as few parameters as possible.

 

The most carefully thought-out model is worthless if you can’t estimate it with the data available. You might think that estimating four parameters with thirty data points is not asking too much of the data. However, experience has shown that a three parameter model which fits almost as well will forecast better most of the time. This is true even if the difference is statistically significant.

 

Copyright © 2026 Thomas A. Doan