How can you determine the order of a time series regression model?

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Time series regression is a powerful technique for analyzing the relationship between a dependent variable and one or more independent variables over time. However, before you can run a time series regression, you need to determine the order of the model, which means how many lagged terms of the dependent variable and the independent variables you need to include. How can you do that? Here are some steps to help you.

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Check for stationarity:

Use statistical tests like the Augmented Dickey-Fuller to determine if your data's mean and variance are constant over time. This is crucial for ensuring your model's accuracy.
Compare model fits:

Evaluate different models' performance using criteria like the Akaike information criterion. It's like trying on shoes; you pick the one that fits best for a comfortable, blister-free walk.

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Jyotishko Biswas

AI and Gen AI Leader | AI Speaker | 18…
Arijana Amina R.

1 Check for stationarity

Stationarity means that the statistical properties of a time series, such as its mean, variance, and autocorrelation, do not change over time. Most time series regression models assume that the data are stationary, or at least can be transformed to be stationary. To check for stationarity, you can use graphical methods, such as plotting the time series and its autocorrelation function, or statistical tests, such as the Augmented Dickey-Fuller test or the KPSS test. If the data are not stationary, you may need to apply differencing, detrending, or other transformations.

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Jyotishko Biswas

AI and Gen AI Leader | AI Speaker | 18 years exp. in AI | AI Leader Award 2024 (from 3AI) | Indian Achievers Award 2024 (from Indian Achievers Forum) | Forbes Technology Council Member | ex Deloitte, IBM
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Generally I consider weak stationarity which means the mean, standard deviation and covariance are constant over time for the time series data. It's an important assumption for time series modeling. We prefer to make the time series stationary instead of neglecting this assumption. There are methods to make a time series stationary. I often plot mean and standard deviation over time and decide whether data is stationary. However, nowadays we build productionalised AI applications. For these applications we use dickey fuller test. That way we avoid a human looking into the plots and then decide whether the data needs to be made stationary.

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Eren Unlu

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If you do not want to go with ADF and KPSS, actually assessing stationarity and homoskedesticity is somewhat simple with basic graphical evaluation. For instance you can also use moving average filters to check means and standard deviation.

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Arijana Amina R.
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For me, analysing visual plotting of the data and some basic statistics (mean, variance, st.dev, correlations) was enough to check for stationarity. By using visualization, i got feeling of the data and this i used later for determining appropriate method or influential variables.

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2 Identify potential predictors

The next step is to identify the potential independent variables that may affect the dependent variable over time. These can be other time series, such as economic indicators, weather variables, or seasonal factors, or dummy variables, such as interventions, events, or structural changes. You can use scatter plots, cross-correlation functions, or Granger causality tests to explore the relationship between the potential predictors and the dependent variable.

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Arijana Amina R.
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As already mentioned by stationarity checking, using visual plotting of the data and basic statistics (especially relations) between the variables of interest helped me to identify the potential predictors. Of course sometimes i used to run same time series analysis method using different predictors and check for the results and compare them to see what changes and what influences my model. It helped me to finally determine the predictors.

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3 Choose a model form

Depending on the nature of the data and the research question, you may choose different forms of time series regression models. Some common forms are autoregressive (AR), moving average (MA), autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA), and seasonal autoregressive integrated moving average (SARIMA). These models differ in how they account for the lagged effects of the dependent variable and the error terms, as well as the degree of integration and seasonality.

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Arijana Amina R.
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With a lot of analysis and application of different models, over time you just get the feeling about proper model depending on the variables and the research theses. Check the different models using possibly same predictors and analyze your results for getting the feeling about their differences and possibilities.

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4 Estimate the model parameters

Once you have chosen a model form, you need to estimate the parameters of the model, such as the coefficients of the lagged terms and the error terms. You can use various methods, such as ordinary least squares (OLS), maximum likelihood estimation (MLE), or Bayesian estimation. You can also use software packages, such as R, Python, or Stata, that provide functions for fitting time series regression models.

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Arijana Amina R.
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I just want to correct here this one sentence "you can also use software packages, such as R,..."... it should be said "you can also use existing software packages, for example in R..." (R has many packages and it is not a package itself)

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5 Evaluate the model fit

The final step is to evaluate how well the model fits the data and meets the assumptions of time series regression. You can use various criteria, such as the coefficient of determination (R-squared), the Akaike information criterion (AIC), or the Bayesian information criterion (BIC), to compare different models and select the best one. You can also use diagnostic plots, such as residual plots, Q-Q plots, or Ljung-Box tests, to check for normality, homoscedasticity, and independence of the error terms. If the model does not fit well or violates the assumptions, you may need to revise the model form, add or remove predictors, or apply transformations.

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Arijana Amina R.
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This is the analysis i mentioned before. This step is kind of always needed. I never allowed myself to blindly run one model and take its result for granted. I always run some more models and "plaid" with the predictors or parameters before i decided which model was the best fit.

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6 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?

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How can you determine the order of a time series regression model?

1

2

3

4

5

6

1 Check for stationarity

2 Identify potential predictors

3 Choose a model form

4 Estimate the model parameters

5 Evaluate the model fit

6 Here’s what else to consider

Statistics

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How can you determine the order of a time series regression model?

1

2

3

4

5

6

1 Check for stationarity

2 Identify potential predictors

3 Choose a model form

4 Estimate the model parameters

5 Evaluate the model fit

6 Here’s what else to consider

Statistics

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