# Linear Regression vs. ARIMA

I have a data set that was sampled at a high frequency relative to the speed over which changes are expected to occur. This has resulted in high autocorrelation between adjacent values upto a lag of 200-300. The goal of my project is to measure the magnitude of intervention effects on this large time series.

Initially I tried to use a linear regression with autoregressive coefficents, but switch to an arima with exogenous regressors. What is the practical difference in the use of these two approaches?or are they effectively equivalent? I have been hard pressed trying to find direct comparisons of the benefits and costs of each.

• You might want to start with my response to a similar question stats.stackexchange.com/questions/166640/… . Depending on how you set up your "exogenous regressors" they can be the same BUT you question is vague Commented Dec 9, 2017 at 16:28
• Hi there! Just a quick comment about smoothing and such. With smoothing, you're effectively throwing away data points. How do you know those data points don't contain valuable information in prediction or probability of another variable? Unless the data was measured with error, you might want to reconsider smoothing; or do the analysis with and without the smoothed data and compare the 2 models. Commented Dec 9, 2017 at 16:35
• What exactly do you mean by regression with autoregressive coefficients? And what with arima with exogenous variables? Can you write down both models in equation form? Because to me it sounds as the same?
– user83346
Commented Dec 9, 2017 at 19:02

First, your high number of lags is not uncommon. It might be an artifact of the frequency. Box & Jenkins (1970) recommend a maximum of n/4 meaningful lags and Cowpertait & Metcalfe (2009) claim that the number of meaningful lags is no more than the frequency.

Second, ARIMA stands for Auto Regressive Integrated Moving Average. So a linear repression with autoregressive coefficients (I'm also not sure what that might mean, exactly) would not have a moving average term like ARIMA might. It also would not include a differencing parameter to ensure stationarity.

When you say 'practical' difference, that depends on your field. Results for a pharmacological study would be interpreted different than one for psychotherapy.

• This does not appear to answer the question.
– mkt
Commented Dec 9, 2017 at 21:17
• I've edited the answer Commented Dec 9, 2017 at 21:51