How do you fix time series regression models?

1 Check for autocorrelation

Autocorrelation is the correlation of a variable with itself at different time lags. It can cause biased estimates and inflated standard errors in regression models. To check for autocorrelation, you can plot the residuals of your model and use the Durbin-Watson test or the Ljung-Box test. If you find evidence of autocorrelation, you can try to fix it by using a different model specification, such as adding lagged variables or using a generalized least squares (GLS) approach.

2 Test for stationarity

Stationarity means that the statistical properties of a time series, such as the mean, variance, and autocorrelation, are constant over time. Non-stationary time series can lead to spurious regression results and unreliable forecasts. To test for stationarity, you can use the Augmented Dickey-Fuller (ADF) test or the Phillips-Perron (PP) test. If you reject the null hypothesis of these tests, it means that your time series is stationary. If not, you can try to transform your time series by differencing, detrending, or applying a logarithmic or power function.

3 Handle seasonality

Seasonality is the periodic variation of a time series due to factors such as weather, holidays, or business cycles. It can affect the interpretation and prediction of your regression model. To handle seasonality, you can use a seasonal adjustment method, such as the X-13ARIMA-SEATS or the Census method, to remove the seasonal component from your time series. Alternatively, you can use a seasonal dummy variable or a seasonal decomposition model, such as the additive or multiplicative model, to account for the seasonal effect in your regression model.

4 Adjust for heteroskedasticity

Heteroskedasticity means that the variance of the error term in your regression model is not constant across time or across the values of the independent variables. It can cause inefficient and inconsistent estimates and invalid inference. To adjust for heteroskedasticity, you can use a robust standard error method, such as the White or the Newey-West method, to correct the standard errors of your coefficients. Alternatively, you can use a weighted least squares (WLS) method to give more weight to observations with lower variance and less weight to observations with higher variance.

5 Validate your model

After you fix the problems with your time series regression model, you need to validate your model to ensure that it fits the data well and can make accurate predictions. To validate your model, you can use various measures and tests, such as the R-squared, the adjusted R-squared, the root mean squared error (RMSE), the Akaike information criterion (AIC), the Bayesian information criterion (BIC), and the forecast error variance decomposition (FEVD). You can also use cross-validation or out-of-sample validation techniques to assess the performance of your model on new data.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?