Challenges of using time series forecasting to predict inflation
The main issue with using exogenous variables to forecast inflation is that inflation is impacted by a myriad of different factors - and no one model could possibly account for all of them.
In addition, the issue with attempting to predict inflation using time series forecasting methods is that inflation (or any macroeconomic variable) tends to be more of a stochastic time series with inherent randomness as opposed to deterministic - where there is a clearly defined pattern over time.
As a contrasting example, let us take an example of forecasting weather data vs. inflation.
Here is an autocorrelation function generated using statsmodels in Python for monthly weather data.
We can see that there is a clear seasonal trend in correlation every 12 months - as we would expect since cold temperatures in January are likely to be similar to that of the previous January, July temperatures will be similar to that of last July, etc.
However, let us now look at an autocorrelation function generated using yearly U.S. inflation data from 1960-2019 as sourced from fred.stlouisfed.org:
We can see that there is no particular seasonal pattern to inflation, as evidenced by the drop-off in autocorrelations as the time lags increase.
In this regard, when predicting using auto_arima for the first 40 years of data and then predicting on the last 20 - ARIMA(0,1,3)(0,0,0)[0] was selected as the best fit. This essentially means that the model is forecasting a random walk as below:
Alternative solution: Detecting causal inference between macroeconomic variables
The challenge here is that i would like to establish the connection
between these variables and inflation (which exist according to the
Central bank)
If this is the case, then the recommended path is not necessarily using forecasting methods to predict the time series, but in implementing causal inference to establish the degree to which a relationship exists between two variables.
Let's consider an example. Suppose that one wishes to investigate the relationship between fluctuations in exchange rates and inflation. This could be accomplished using CausalImpact, which uses Bayesian structural time-series models to detect casual inference. This package can be implemented in either Python or R.
Here is an example of how one might apply the model. Let us suppose that one wishes to investigate whether there is a relationship between European inflation and an intervention, e.g. a change in ECB interest rates. To do this, one would need to select a control time series that would not be affected by the intervention. For instance, one would hypothesise that Japanese inflation rates would not be impacted by changes in ECB interest rates. Therefore, Japanese inflation rates could be used as a control variable - and using causal inference would seek to answer the question - what would happen to inflation if the interest rate change had not taken place?
By establishing this, one could then seek to establish causal inference and attempt to quantify the degree to which a change in one variable impacts another.
Disclaimer: The examples in the above answer are given merely to facilitate the explanation of time series principles - none of the above is intended as any sort of financial or investment advice.
