Module 10 of 1255 min readIntermediate

Time series operators and ARIMA

tsset, the L. F. D. operators, tsline, dfuller for unit roots, arima, and forecasting basics.

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Learning objectives

By the end of this module, you should be able to:

01Declare a time variable with tsset and use the L., F., D. operators for lag, lead, and difference
02Test for unit roots with the Augmented Dickey-Fuller test (dfuller)
03Fit ARIMA models and generate forecasts
04Plot time series with tsline and recognise stationarity issues visually

Time series in Stata: tsset declares the time variable, time-series operators (L. F. D.) reference past, future, and difference values, dfuller tests for unit roots, and arima fits the standard time-series models.

tsset

stata

tsset month, monthly
tsset year, yearly

Lag, lead, difference operators

stata

generate lag1 = L.cpi              // 1-period lag
generate lag12 = L12.cpi           // 12-period lag
generate lead1 = F.cpi             // 1-period lead
generate diff1 = D.cpi             // first difference
generate diff12 = D12.cpi          // 12-period difference (year-over-year change)

generate growth = (cpi / L12.cpi - 1) * 100   // YoY % change

tsline — time series plotting

stata

tsline cpi
tsline cpi, name(g1)
tsline cpi lending_rate, name(g2)

Unit roots: dfuller

stata

dfuller cpi                                // Augmented Dickey-Fuller, no constant
dfuller cpi, trend                          // with trend
dfuller cpi, lags(4)                        // 4 lagged differences

* Reject H0 (unit root) → variable is stationary
dfuller D.cpi                              // test in first differences

ARIMA

stata

arima cpi, arima(1, 1, 1)         // ARIMA(p, d, q): AR=1, integrated=1, MA=1
estat ic                          // information criteria for model selection

Forecasting

stata

arima cpi, arima(1, 1, 1)
predict yhat
predict resid, residuals
forecast list                              // built-in forecast diagnostics

First-difference if non-stationary, then model

If dfuller fails to reject the unit root, take first differences (D.cpi) and re-test. Models on stationary data give valid inference; models on non-stationary data give spurious regressions.

Exercise

Compute the year-over-year growth rate of cpi.

Key takeaways

◆tsset month, monthly declares a monthly time series; daily/weekly/quarterly/yearly all supported
◆L.x is the lag; D.x is the first difference; D12.x is the 12-period difference (year-on-year)
◆dfuller H0 = unit root; failing to reject means non-stationary — take first differences and re-test
◆Modelling on non-stationary data produces spurious regressions — always check for stationarity first