I'm trying to perform a hypothesis test for an arima forecast, and I haven't been able to find resources for it. Below is a reproducible example of my data. I'm using a zoo time series because my frequency is weekdays only.
The hypothesis test I'd like to perform is:
H1: The forecasted value is greater than a specified value which I'd provide,
H0: There is no difference in values.
library(timeDate)
library(forecast)
library(zoo)
library(magrittr)
set.seed(12345)
dates=timeSequence('2017-09-01','2017-09-08')
dates=dates[isWeekday(dates)]%>%as.character()%>%as.POSIXct()
# Need to drop the timeDate class
values=rnorm(n=6,mean=12500,sd=500)
cumValues=cumsum(values)
zooObj=zoo(cumValues,dates)
arimaModel=auto.arima(zooObj)
So for this data, the predicted next value is:
> forecast(arimaModel,h=1)
Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
1504929600 83612.53 78117.67 89107.39 75208.87 92016.19
I'd like to hypothesis test the probability that the next value is greater than 83,000.