I have a question related to the estimation of arima models in R. I have estimated a model with daily simulated data where Mondays have a lower value than the rest of the days. I have simulated two years of data, and I want to predict the next year.
According to the data, I should obtain an estimation which has lower values on Mondays, but I get it on Tuesdays... It seems the data has been desplaced one day. I show my code.
library(ggplot2)
library(forecast)
library(lubridate)
date <- seq(as.Date('2018-01-01'),as.Date('2019-12-31'),by='day')
orders <- rnorm(length(date),100,10)
s <- seq(1,length(date),by=7)
for(i in s)
{
orders[i] <- orders[i]-rnorm(1,70,10)
}
datos <- data.frame(date = date,orders = orders)
ggplot()+
geom_line(data = datos, aes(x = date, y = orders))
datos begins on Monday 2018-01-01. Every Monday has a lower value. Now I estimate the model with the corresponding seasonal periods.
orders_ts <- msts(datos$orders,seasonal.periods = c(7,365.25),start = decimal_date(as.Date("2018-01-01")))
model <- auto.arima(orders_ts,trace = T,D=1)
pred <- forecast(model,h=365)
plot(pred)
pred_tabla <- as.data.frame(pred)
date_pred <- as.Date(time(rownames(pred_tabla)), origin = "2019-12-31")
rownames(pred_tabla) <- date_pred
pred_tabla <- dplyr::select(pred_tabla,c('Point Forecast'))
colnames(pred_tabla) <- 'Prediction'
head(pred_tabla,50)
Prediction
2020-01-01 89.65607
2020-01-02 127.10014
2020-01-03 104.69489
2020-01-04 104.82119
2020-01-05 90.43497
2020-01-06 119.54629
2020-01-07 28.30212
2020-01-08 76.84848
2020-01-09 89.47474
2020-01-10 108.30905
2020-01-11 108.61325
2020-01-12 79.79830
2020-01-13 82.68802
2020-01-14 30.47466
2020-01-15 83.57336
2020-01-16 104.82201
2020-01-17 94.73705
2020-01-18 97.66296
2020-01-19 94.98595
2020-01-20 99.00874
2020-01-21 43.39133
2020-01-22 110.69250
2020-01-23 99.88973
2020-01-24 91.25167
2020-01-25 86.29674
2020-01-26 99.76741
2020-01-27 96.38425
2020-01-28 17.60269
2020-01-29 99.22064
2020-01-30 116.89777
2020-01-31 114.49706
2020-02-01 108.64221
2020-02-02 114.64886
2020-02-03 88.54560
2020-02-04 17.62015
2020-02-05 101.96455
2020-02-06 97.18976
2020-02-07 100.91465
2020-02-08 94.81816
2020-02-09 103.15029
2020-02-10 100.13627
2020-02-11 32.48818
2020-02-12 97.34060
2020-02-13 99.69957
2020-02-14 82.02583
2020-02-15 89.17326
2020-02-16 93.99973
2020-02-17 98.01702
2020-02-18 34.04982
2020-02-19 91.95284
Now the lower values are on Tuesdays, in 2020-01-07, 2020-01-14, etc.
Could someone give me an answer of why this is happening? And how could I solve this?
Thank you very much!
