I have a financial time series,
x, it's length is
n=8 observations only. Each observation corresponds to the quarterly costs (numerical value) of a firm. I need to predict future costs and find 95% confidence interval on the next quarter.
x <- c(1122156.70, 777243.30, 741537.90, 1160976.40, 1316723.00, 781010.00, 70447.00, 1413481.00) plot(x, xlab='Quarters', ylab='Cost, USD')
From the plot you can assume in this series that there exists a seasonal component.
My intuition is: to split the quarterly value on the month one, and then apply some method (for example non-linear regression) to predict future costs. For simplicity let's split under assumption of the uniform distibution. For instance,
x1 <-rep(x/3, each=3) # uniform split on 3 length(x) # 8 length(x1) # 24
In this case I'll have $n=24$ observations.
Of course you can say it's impossible to do an adequate prediction on such a tiny sample.
Question. Could you please share your point of view on the problem?