How to estimate time series model when data are stationary after first difference?
If the data are stationary after first difference, you can estimate a time series model using the first difference of the data.
Hi,
I suppose your question is how to proceed with modelling such data.
Regarding what you mentioned about stationarity, in time series notation (1-B)Yt, i.e. first difference of your data, follows an ARMA(p,q).
Your task is now, a) choosing best p and q, as model parameters by fitting this model to you transformed data, then b) the residuals of your model needs to investigated using the residual diagnostics analysis.
I recommend you have a look at "auto.arima" in "forecast" package in R software followed by "tsdiag" functions in R.
Among others, reading the following book is recommended.
Forecasting: Principles and Practice (3rd ed)
https://otexts.com/fpp3/
good luck,
Yours,
Hamid
Khemraj Subedi
Hello
Since your variables have same degree of integration, use the co-integration test.
If there is a long-term relationship between the variables, you can use the level of the variables in the estimation.
I presume that your data are I(1) in levels. Does economic theory predict that there is/are long-term relationship(s) between any of the data? You can then test and test these long-term relationships using Engle-Granger, Johansen, ARDL as appropriate.
Then
I would recommend that you consult a text such as Enders's Introduction to Econometric time series analysis. This is a topic that is difficult and it is very easy to go very wrong applying various recipes in econometric packages. I would stress that you need to specify and understand the economic problem that you are addressing. Any conclusions that you come to are conditional on the correctness of that model. The model should dictate what econometrics you use and what you can infer.
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