# Solved – Forecasting with holiday dumthe variables

I have an example of call center data for 2013. There are 261 days of data (excluding weekends).
For 2013, I have included a holiday dummy variable (`holiday`) for the days where there were no stats.
For 2014, I have also included a future holiday dummy variable (`holidayf`).
My objective is to assess how accurate this code is in making predictions for 2014.

I tried this code below but when looking at `fc\$fitted`, the forecasts don't seem to be correct. For the first 8 days of January 2014, it forecasts the exact number of calls that were received in the first 8 days of January 2013, which seems wrong. Also, where there is a public holiday in 2014, the future forecast for that day predicts a normal to high volume of calls, so it seems that the forecast is using the `holiday` variable and not the `holidayf` variable.

``library(forecast) y <- ts(calls,frequency=5) z <- fourier(ts(calls,frequency=261),K=12) zf <- fourier(ts(calls,frequency=261),K=12,h=261) fit <- auto.arima(y,xreg=cbind(z,holiday)) fc <- forecast(fit,xreg=cbind(zf,holidayf),h=261) plot(fc) ``

Data:

``calls <-    c(0,145,175,129,266,219,156,184,167,241,218,194,192,162,236,219,212,191,162,216,   235, 218,180,150,245,209,210,211,151,236,197,217,140,164,200,156,152,153,141,224,178,   159,153,137,207,173,197,213,206,305,284,248,289,269,359,333,257,0,244,325,292,267,   206,0,0,360,261,327,284,385,377,317,327,271,372,191,320,268,261,376,320,280,251,200,   200,200,0,236,161,259,200,190,166,174,225,228,202,201,155,241,207,199,179,178,249,   243,230,177,181,264,250,219,204,178,244,249,185,184,164,0,253,216,217,165,170,185,   175,160,148,231,223,196,162,149,228,213,190,177,139,212,205,221,190,170,196,210,   198,192,131,220,185,199,153,166,240,176,200,145,0,255,202,220,220,181,250,171,164,   142,118,179,197,167,130,124,180,214,203,153,140,161,200,191,159,141,227,170,166,   166,106,131,0,176,156,109,196,175,175,174,161,230,191,159,150,91,180,188,173,157,   107,193,172,172,172,116,195,183,169,146,125,208,160,160,177,128,191,176,149,175,   136,217,162,178,130,99,158,154,135,146,106,155,148,119,137,96,161,106,114,139,84,   0,97,95,82,65,59,23,0,0,48,83,48)    holiday <- c(1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,              0,0,0,0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,              0,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,              0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,              0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,              0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,              0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,              0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,              0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,              0,0,0,1,1,1,0,0,0)   holidayf <- c(1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,              0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,              0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,              0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,              0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,              0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,              0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,              0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,              0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,              0,0,0,0,1,1,0,0,0) ``
Contents

Read `?forecast.Arima` closely. `fc\$fitted` does not give the forecast, it gives the in-sample fits. These are identical to the history at the beginning, because the rather complex ARIMA(2,0,2)(1,0,2)[5] model that `auto.arima()` finds needs an amount of differencing to fit the seasonality.
Use `fc\$mean` to extract the point forecasts. Note that the graph also shows forecasts that are appreciably different from the history. Notably, you get negative values. Given that all historical values are nonnegative, you may want to think about constraining your forecasts in some way.