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I am trying to perform interrupted time series analysis using an ARIMA model based on the following paper: Interrupted time series analysis using autoregressive integrated moving average (ARIMA) models: a guide for evaluating large-scale health interventions

One issue I am running into however is whether or not my ARIMA model can include more than one exogenous variable without introducing multicollinearity and inflating the variance of the coefficient estimates. If I run a model with an exogenous variable for S_t (A sudden, sustained change where the time series is shifted either up or down by a given value immediately following the intervention. The step change variable takes the value of 0 prior to the start of the intervention, and 1 afterwards) and R_t (A change in slope that occurs immediately after the intervention. The ramp variable takes the value of 0 prior to the start of the intervention and increases by 1 after the date of the intervention) would that introduce multicollinearity making my results invalid? Should I only run a model with one of these variables at a time?

One way to resolve this that I thought of was to modify R_t (let's call this variable R_t_prime) to increase only after the previous S_t was 1 (ie when S_t is 1 the first time, R_t will be 0, then on the following entry S_t will be 1, and R_t will be 1). Would this remove the relationship between R_t and S_t because S_t can no longer be made via a boolean operation on R_t? Would the model with R_t_prime be more valid because it does not introduce multicollinearity?

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    $\begingroup$ Re "without inflating:" the point to introducing a new variable is to improve the model, which usually includes a decrease in the estimation variance of any parameter of interest. The issue therefore is not whether multicollinearity in itself will degrade the variance, but only whether including the variable is a net improvement. Moreover, any such "inflation," however you might measure it, does not make your results "invalid." Thus, your concerns appear premature and perhaps irrelevant. BTW, the two-model approach is no solution and likely to be worse. $\endgroup$
    – whuber ♦
    Commented Aug 28 at 14:59

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To clarify you are asking about whether running a model where the design matrix has two columns which are:

S_t R_t
0 0
0 0
0 0
0 0
0 0
1 1
1 2
1 3
1 4
1 5
1 6

Would induce colinearity? I see that this is what is suggested in the paper. Is your proposal to shift R_t by 1 to completely distinguish the ramp change (time increasing effect) from the sustained change as below:

S_t R_t_prime
0 0
0 0
0 0
0 0
0 0
1 0
1 1
1 2
1 3
1 4
1 5
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  • $\begingroup$ As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Commented Aug 26 at 15:17

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