R time-series forecasting with auto.arima and xreg=explanatory variables

I have lots of time-series (retail data) and I want to make forecast for all of them.

For example let's take a look at one of them:

   > dput(x)
 c(1774, 1706, 1288, 1276, 2350, 1821, 1712, 1654, 1680, 1451, 
 1275, 2140, 1747, 1749, 1770, 1797, 1485, 1299, 2330, 1822, 1627, 
 1847, 1797, 1452, 1328, 2363, 1998, 1864, 2088, 2084, 594, 884, 
 1968, 1858, 1640, 1823, 1938, 1490, 1312, 2312, 1937, 1617, 1643, 
 1468, 1381, 1276, 2228, 1756, 1465, 1716, 1601, 1340, 1192, 2231, 
 1768, 1623, 1444, 1575, 1375, 1267, 2475, 1630, 1505, 1810, 1601, 
 1123, 1324, 2245, 1844, 1613, 1710, 1546, 1290, 1366, 2427, 1783, 
 1588, 1505, 1398, 1226, 1321, 2299, 1047, 1735, 1633, 1508, 1323, 
 1317, 2323, 1826, 1615, 1750, 1572, 1273, 1365, 2373, 2074, 1809, 
 1889, 1521, 1314, 1512, 2462, 1836, 1750, 1808, 1585, 1387, 1428, 
 2176, 1732, 1752, 1665, 1425, 1028, 1194, 2159, 1840, 1684, 1711, 
 1653, 1360, 1422, 2328, 1798, 1723, 1827, 1499, 1289, 1476, 2219, 
 1824, 1606, 1627, 1459, 1324, 1354, 2150, 1728, 1743, 1697, 1511, 
 1285, 1426, 2076, 1792, 1519, 1478, 1191, 1122, 1241, 2105, 1818, 
 1599, 1663, 1319, 1219, 1452, 2091, 1771, 1710, 2000, 1518, 1479, 
 1586, 1848, 2113, 1648, 1542, 1220, 1299, 1452, 2290, 1944, 1701, 
 1709, 1462, 1312, 1365, 2326, 1971, 1709, 1700, 1687, 1493, 1523, 
 2382, 1938, 1658, 1713, 1525, 1413, 1363, 2349, 1923, 1726, 1862, 
 1686, 1534, 1280, 2233, 1733, 1520, 1537, 1569, 1367, 1129, 2024, 
 1645, 1510, 1469, 1533, 1281, 1212, 2099, 1769, 1684, 1842, 1654, 
 1369, 1353, 2415, 1948, 1841, 1928, 1790, 1547, 1465, 2260, 1895, 
 1700, 1838, 1614, 1528, 1268, 2192, 1705, 1494, 1697, 1588, 1324, 
 1193, 2049, 1672, 1801, 1487, 1319, 1289, 1302, 2316, 1945, 1771, 
 2027, 2053, 1639, 1372, 2198, 1692, 1546, 1809, 1787, 1360, 1182, 
 2157, 1690, 1494, 1731, 1633, 1299, 1291, 2164, 1667, 1535, 1822, 
 1813, 1510, 1396, 2308, 2110, 2128, 2316, 2249, 1789, 1886, 2463, 
 2257, 2212, 2608, 2284, 2034, 1996, 2686, 2459, 2340, 2383, 2507, 
 2304, 2740, 1869, 654, 1068, 1720, 1904, 1666, 1877, 2100, 504, 
 1482, 1686, 1707, 1306, 1417, 2135, 1787, 1675, 1934, 1931, 1456)

I want to make a forecast with auto.arima model:

y=auto.arima(x)
plot(forecast(y,h=30))
points(1:length(x),fitted(y),type="l",col="green")

enter image description here

There are abnormally high sales near indices 280-300. I know, that there were some fests. I want to feed those to my forecasting model as explanatory variables.

I have a vector holiday, where TRUE --- explanatory variables.

> dput(holiday)
c(FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, 
TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE)

I try to add that explanatory dates to the model:

> auto.arima(x, stepwise=FALSE,approx=FALSE, xreg=holiday)
Series: x 
ARIMA(2,1,3)                    

Coefficients:
          ar1      ar2      ma1     ma2      ma3    holiday
      -0.4682  -0.9568  -0.2008  0.4029  -0.8424  -354.5092
s.e.   0.0173   0.0169   0.0398  0.0338   0.0412   112.5610

sigma^2 estimated as 85849:  log likelihood=-2245.74
AIC=4505.49   AICc=4505.85   BIC=4531.8

Seems like it is working, but when I try to plot it fails with error:

y<-auto.arima(x, stepwise=FALSE,approx=FALSE, xreg=holiday)
> plot(forecast(y,h=30))
Error in plot(forecast(y, h = 30)) : 
  error in evaluating the argument 'x' in selecting a method for function 'plot': Error     in forecast.Arima(y, h = 30) : No regressors provided

Maybe I'm doing something wrong? how can I add explanatory variables to the model and then plot forecast?

Can you use ARIMA for multivariate?

ARIMAX is an extended version of the ARIMA model which utilizes multivariate time series forecasting using multiple time series which are provided as exogenous variables to forecast the dependent variable.

How do you forecast the time series with ARIMA model?

Step 1 — Check stationarity: If a time series has a trend or seasonality component, it must be made stationary before we can use ARIMA to forecast. . Step 2 — Difference: If the time series is not stationary, it needs to be stationarized through differencing. Take the first difference, then check for stationarity.

Is SARIMA better than ARIMA?

Since SARIMA brings in seasonality as a parameter, it's significantly more powerful than ARIMA in forecasting complex data spaces containing cycles.

When should you not use ARIMA?

💾 ARIMA requires a long historical horizon, especially for seasonal products. Using three years of historical demand is likely not to be enough. Short Life-Cycle Products. Products with a short life-cycle won't benefit from this much data.

You have to provide the regressor values in the forecast period as well:

fcast <- forecast(y, h=30, xreg=data.frame(holiday=rep(FALSE,30)))
fcast
plot(fcast)

R time-series forecasting with auto.arima and xreg=explanatory variables

Tags:

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time-series

forecasting

Marta

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Stephan Kolassa

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R time-series forecasting with auto.arima and xreg=explanatory variables

Tags:

r

time-series

forecasting

Marta

People also ask

1 Answers

Stephan Kolassa

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Recent Activity

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