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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)
#[1] 8
length(x1)
#[1] 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?

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  • $\begingroup$ Could you clarify what you expect to gain by "splitting" the quarterly data into months? You don't really have 24 observations at that point because you really haven't obtained any additional information. The assumption that each month in a seasonal, quarterly financial series is constant is also unlikely to be true, in any case. $\endgroup$ – Chris Haug Nov 12 '16 at 1:57
  • $\begingroup$ Thanks for the comment. I hope to increase a size sample. Uniform splitting is the assumption only. I can split into three unequal terms which sum equals to the quartel value, $\endgroup$ – Nick Nov 12 '16 at 2:46
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Your approach won't work. To convince yourself imagine that you had only a single value and repeated it one thousand times to have a sample of one thousand. Would single value repeated one thousand times have any additional information value? Actually many software packages will throw errors when encountering such zero-variance data. You can also check this thread that describes similar idea and it's shortcomings.

For learning more about dealing with short time-series check my question and the great answers it received: Best method for short time-series

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