In this blog we are going to talk about moving average model and analyse the ‘logan_intl_flights’ time-series from Analyze Boston.

The Moving Average Model, or MA(q) for short, is a part of the larger class of time series analysis models known as ARIMA (Autoregressive Integrated Moving Average) models. By taking into account the impact of random or “white noise” terms from the past, this model forecasts the current observation. The number of historical white noise terms taken into consideration is indicated by the model’s order, denoted by “q” in MA(q). For example, the latest white noise term is considered in MA(1).

Features of the Model: The current observation is expressed by the model’s mathematical equation as a linear combination of the current white noise term and the most recent q white noise terms. A series of independent, identically distributed random variables with a constant variance and zero mean is known as white noise. In order for the MA(q) model to be applicable, the time series must display a constant mean (μ). Furthermore, stationarity is required, and if needed, differencing can be used to attain it. Model identification, or order q, is determined using methods such as autocorrelation function (ACF) plots and statistical criteria. An essential part of applying MA(q) to time series analysis is parameter estimation, followed by forecasting and model validation using techniques like residual analysis.

Now we are going to use MA(1) model on our ‘logan_intl_flights’ time series

The Autocorrelation Function (ACF) plot shows correlation coefficients on the y-axis and the number of lags, or the interval of time between the current observation and its lagged values, on the x-axis. An ACF plot attempts to identify significant spikes that decrease with increasing lags. A notable spike at a particular lag indicates a strong correlation with observations at that lag. Comparably, the Partial Autocorrelation Function (PACF) plot uses the same idea for the x-axis but uses the y-axis to show partial correlation coefficients. By eliminating the impact of intermediate lags, PACF isolates the distinct correlation between the current observation and its lagged values. Notable peaks in the PACF plot reveal robust partial correlations at those lags, shedding light on how each lag directly affects the current observation. In essence, the ACF provides information about how each lag affects times that come after, whereas the PACF shows the direct effect of each lag on the current time.