The autoregressive moving average (ARMA) is a common technique in time series analysis. In my view, a time series example that can be suitable with the ARMA model but need to be revisited is inflation. The model commonly used in inflation data modeling might associate with the relatedness of the variable with its past values. The ARMA model can be used to forecast inflation, and its simple structure that only requires current and past inflation data might offer several advantages. For example, the ARMA (p, q) model forecasts inflation at a given period by linearly projecting the inflation from the previous period to the period in question (autoregressive or AR part) and incorporating white noise from the current period to a certain number of periods back (moving average or MA part). Moreover, the ARMA model used for short-term forecasting tends to perform better on average compared to medium-term forecasting (Stovicek, 2007).
However, there are some considerations before applying the ARMA model to the inflation case. First, determining the model specification can be challenging since the ARMA model might lack a theoretical foundation. Although economic theory suggests that factors like money supply, nominal appreciation, and output gaps influence inflation, the ARMA model might not explicitly incorporate these insights. Moreover, one study found that the US CPI inflation is effectively represented by an unobserved components model with time-varying volatility in both the transitory and trend equations, implying the need to update the ARMA framework to incorporate a time-varying second moment (Stock and Watson, 2007).
Second, it is worth noting that ARMA can only be applied if the stationarity assumption holds. In the absence of stationarity in inflation data, it may be more appropriate to choose ARIMA to induce stationarity. Third, in cases where inflation occurs seasonally due to special events like Christmas or other holidays, other models might outperform ARMA. For example, previous literature suggests that SARIMA could be a better choice in such scenarios (Davidescu et al., 2021). SARIMA models offer advantages over ARIMA models when dealing with data that exhibits strong seasonal patterns, such as higher prices that can be expected during certain months due to holidays or seasonal demand. SARIMA models can capture this effect and adjust the forecasts accordingly, and can also handle multiple seasonal cycles, such as weekly, monthly, and yearly patterns.
Fourth, monetary policy interventions can also influence inflation, leading to structural shocks or breaks. It might be pivotal to consider the sample period and subset the data if necessary to ensure there are no obvious structural breaks, particularly in the case of developed economies. Inflation in advanced economies might be primarily determined by the monetary policy stance of the central bank, such as the Federal Reserve in the case of the US. Additionally, a shift in the monetary policy regime during the sample period might also indicate structural breaks in the data.
Lastly, as central banks target a specific inflation rate, an inflation series should be stationary with a long-run mean centered at the target rate. In most cases, inflation series are highly persistent due to economic reasons. Therefore, before applying Box-Jenkins forecasting techniques, inflation series are typically differenced again. In other words, forecasting is usually conducted for inflation growth rather than inflation levels. To summarize, it might be beneficial to fit various models and compare them using appropriate model selection criteria to determine the best model for inflation forecasting purposes.
References
Davidescu, A. A., Apostu, S. A., & Stoica, L. A. (2021). Socioeconomic effects of COVID-19 pandemic: exploring uncertainty in the forecast of the Romanian unemployment rate for the period 2020–2023. Sustainability, 13(13), 7078.
Stock, J. H., & Watson, M. W. (2007). Why has US inflation become harder to forecast?. Journal of Money, Credit and Banking, 39, 3-33.
Stoviček, K. (2007). Forecasting with ARMA Models: The case of Slovenian inflation. Bank of Slovenia.
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