Hi all. I have two time series of two data loggers that take the ambient temperature each 10 minutes. I would like to analyze the data so that with the information of one data logger I can predict the temperature on the other data logger. I am confused of what analysis should I do, since if I use linear regression (temp1~temp2) the assumption of the independence of residuals would be violated. Including a correlated error structure still gives a pattern in the residuals. What analysis would you suggest me? Thank you in advance
Take a look at this paper. Maybe, it is helpful for you:
https://academic.oup.com/intqhc/article/33/1/mzab050/6178233
Hi Luis, there is a huge variety of alternatives. In what follows some very basic approaches. First, it could be nice to use linear regression between 2 different time series as far they are not integrated or are cointegrated. Moreover, another easy solution for forecasting temp1 is to use a standard ARIMA model with exogenous covariate (ARMA-X) where your covariate is temp2. Furthermore, you can also use a bivariate VAR model at this aim. To get started, a nice reading is the textbook "Forecasting: principles and practice" written by Rob J Hyndman and George Athanasopoulos. You can find it at the following link: https://otexts.com/fpp2/
I suggest using VAR (vector autoregressive) or VARMA models.
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