Solved – Interpreting ARIMA for Interrupted Time Series Analysis

intervention-analysisrtime series

I want to test for efficacy of an intervention. I have pre- and post-intervention data and I used auto.arima to find the best fit for the two data sets.

I'm stuck in the actual use of these models now. What do I do with the auto.arima fit? Can I graph it and test for statistically significant differences in the coefficients? If so, how do I graph it?

This is what I have right now ( specified from auto.arima)

myPreFit<-arima(myPre,order=c(0,1,0))

myPostFit<-arima(myPost,order=c(1,0,1))

Best Answer

Time series intervention analysis is not like this. First, you have to model regular ARIMA model for preintervention period and find the order of appropriate ARIMA model. Then you have to use the order in ARIMAX model (taking whole period, pre+post intervention), including a dummy variable. model1 = forecast::auto.arima(ts_model1, trace = TRUE, seasonal = TRUE, stationary = FALSE,ic = c("aicc", "aic", "bic"),stepwise = TRUE, allowmean = TRUE, allowdrift = TRUE) #ts_model1 is only for preintervention period

Best model: ARIMA(1,1,1)(1,0,0)[12]

model2 = TSA::arimax(ts_model2, order = c(1, 1, 1), seasonal = list(order = c(1, 0, 0), period = 12), xreg = ts_model4, method = c("CSS-ML", "ML", "CSS"), kappa = 1e+06, xtransf =dummy, transfer = list(c(1,0))) I hope you understand.

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Solved – Interrupted time-series analysis for panel data

I would identify the true date of the intervention i.e. when it was fully realized for each state separately using Intervention Detection schemes. The true date (de facto) can often be different from the "known date" (de jure) because of either a pre or a post effect (delay). With a common ARIMA model and one composite intervention variable constructed from the de facto dates, I would then globally estimate all parameters ie. the ARIMA coefficients and the national impact. The coefficient for the composite Intervention Variable would then reflect the national effect. When conducting this Global estimation you need to ensure that the prediction/fitted value for the first reading in the second state is not affected by the latest readings for the first state. For example if the ARIMA model is an AR(12) the first 12 expectations for each state would be the 12 observed values thus generating 12 zero errors. Commercial software with this built-in feature is rare but available.

Solved – Simple interrupted time series analysis

here's the arima function in R.

http://svn.r-project.org/R/trunk/src/library/stats/R/arima.R

snippet you might be interested in:

if (is.null(fixed)) fixed <- rep(NA_real_, narma + ncxreg)
else if(length(fixed) != narma + ncxreg) stop("wrong length for 'fixed'")
mask <- is.na(fixed)
no.optim <- !any(mask)
if(no.optim) transform.pars <- FALSE
if(transform.pars) {
    ind <- arma[1L] + arma[2L] + seq_len(arma[3L])
    if (any(!mask[seq_len(arma[1L])]) || any(!mask[ind])) {
        warning("some AR parameters were fixed: setting transform.pars = FALSE")
        transform.pars <- FALSE
    }
}

Best Answer

Best model: ARIMA(1,1,1)(1,0,0)[12]

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Solved – Interrupted time-series analysis for panel data

Solved – Simple interrupted time series analysis

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