Rolling regression

Overview

The Rolling regression analysis implements a linear multivariate rolling window regression model. Just like ordinary regression, the analysis aims to model the relationship between a dependent series and one or more explanatory series. The difference is that in Rolling regression you define a window of a certain size that will be kept constant through the calculation. The analysis preforms a regression on the observations contained in the window, then the window is moved one observation forward in time and process is repeated. As such, many regressions will be performed as the window is rolling forward.

For more in-depth information regarding the estimation model, please see: Regression analysis

Settings

Regression models

You can define one or more regression models. Each model has separate settings. When a new model is created, the settings of the current model are duplicated. Models can be renamed and deleted.

Include as output

Output dependent series

Select this option to include the dependent series in the output.

Output explanatory series

Select this option to include the explanatory series in the output.

Date range

Start/End range

Specify the limits of the estimation sample range. The default range will be the largest range where there is data for all the series.

Window length

Specify the number of observations to include in the rolling window.

Settings for model

No intercept

When this option is selected, the constant α is omitted from the model and it will be defined as:


  
    
      y
      t
    
    =
    
      β
      1
    
    
    
      
        x
        t1
      
    
    +
    
      
        β
        2
      
      
        x
        t2
      
      +
      
        β
        3
      
      
        x
        t3
      
      +
      
        ϵ
        t
      
    
  

The fact that a rolling window is utilized has implications for the output. When using Regression analysis, a report is generated. In Rolling regression, no such report will be available. This is because, as explained in the overview, a rolling regression constitutes of many regressions, all of which will yield individual statistics. The output of statistics, information criteria and parameters will thus all be time series. You have several options for what information to include in the output.

Outputs for model

Residuals

When this option is selected a series containing the residuals will be included in the output.

Durbin-Watson

The Durbin-Watson is a test statistic used to detect the presence of autocorrelation in the residuals. The value is in the range 0-4. A value close to 2 means that there is little auto correlation. The result from this test is not useful if any dependent series is included with several lags or if no intercept is included in the model.

Schwarz

The Schwarz information criterion takes overfitting into account and estimates the efficiency of the model in terms of predicting the data. The criterion yields a positive value, where a lower value is considered better when comparing different models based on the same data.

R2

The R2 value compares the variance of the estimation with the total variance. The better the result fits the data compared to a simple average, the closer this value is to 1.

Coefficient

The estimated parameters.

P-values

The p-value is the probability of obtaining a value of t that is at least as extreme as the one that was actually observed if the true value of the coefficient is zero.

T-values

The t-value measures the size of the difference relative to the variation in your sample data.

Series settings

Include

Select if you want to include this series in the model.

Is dependent

Select which series is the dependent series. This must be specified.

Diff

Available from version 1.19.

By selecting Diff, the first order differences of the series will be calculated. The result will then be converted back to levels. First order of differences means that the series is transformed to "Change in value" (one observation) while expressing the result in levels.

Lag to/from and Lag range

Here you specify the lags you would like to include for a specific series. If you for example set “Lag from” to 0 and “Lag to” to 2 three series will be included, one series with no lag, one with a lag of 1 and one series with 2 lags. This will automatically change the lag range to “0 to 2”. You may specify the desired lags using Lag to/from or Lag range, the result will be the same. If you set Lag range to a single digit or set Lag to and Lag from to the same value, a single lagged series will be included.

When lags are specified for the dependent series, the lagged series will be used as explanatory series in the model. The dependent series will always be without lag.

Example

Rolling regression

In this example, we used the model presented for the Regression analysis, and created a new regression model which is generated on 5 years rolling window. For the output, we've included the residuals and the R2.