Rolling AR(1) forecasts

The task

Task statement

Sort input.csv by time. Construct one-step-ahead rolling OLS AR(1) forecasts for times f=101,...,250. For each forecast f, use exactly the 100 observed levels y_(f-100),...,y_(f-1). Fit y_s=a+b*y_(s-1) with an intercept on s=f-99,...,f-1, giving exactly 99 regression pairs. Forecast y_f as a_hat+b_hat*y_(f-1). Refit separately at every forecast date using observed values. Score RMSE=sqrt(sum_{f=101}^{250}(y_f-forecast_f)^2/150). Report terms rmse, forecast_101, forecast_150, forecast_200, and forecast_250. Set se=null for every term. For rmse set n_obs=150. For each forecast set n_obs=99, the number of regression pairs used to estimate that forecast's model.

Data

250 ordered observations with columns time (1 through 250) and y.

Files

input.csv

Seed

2026091412

Required output

Scored estimates: rmse, forecast_101, forecast_150, forecast_200, forecast_250.

Reference output

A run succeeds when every scored estimate lies within 1 percent or 0.005 of its reference value, whichever is larger. Sample sizes are not scored.