"an autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model."
A statistical model for time series that incorporates autoregressive, differencing and moving average components.
Time Series Data: The first topic to learn about ARIMA is Time Series data, its components, and its properties. The time series can be defined as a sequence of observations collected over time, and it needs to be explored, and The time series appears in many fields, such as economics, finance, meteorology, and engineering.
Stationarity: Stationarity is an essential concept in time series analysis since many time series models work only when the data is stationary. You should learn why and how to check stationarity of your data, and how to make the data stationary if it's not, either by differencing the data or by transforming the data.
AutoRegression: AutoRegression is a class of time series models that assume that the current value of the series can be modeled as a linear combination of past values and a white noise error term. A significant topic in Autoregressive models is the number of lag terms to include to model the time series accurately.
Moving Average: A moving average is a time series model that focuses on the influence of random white noise on the current observation. It assumes that the current value of the series is influenced by past white noise terms. You should learn how to estimate and interpret the parameters of a moving average model.
Integrated: Integrated is the concept that defines the number of times differencing was taken to make the data stationary. You should learn how to perform differencing to make the data stationary and how to determine the optimal number of times to take the difference.
ARMA: ARMA models are a combination of Autoregressive and Moving Average models, where the current observation is modeled as a sum of past values and past white noise terms. You should learn the notation used to specify an ARMA model, how to estimate the parameters of an ARMA model, and how to use it to make predictions.
Seasonal ARIMA: Seasonal ARIMA models are a combination of Autoregressive, Moving Average, and Seasonal models. It can be used when the time series has a seasonal pattern. You should learn how to specify a seasonal ARIMA model, how to estimate the parameters, and how to make predictions.
Model Selection: There are various optimization techniques used to select the best model that fits the time series data. You should learn how to choose which model is the best fit by using AIC, BIC, and other selection criteria.
Model Diagnostics: The last step in the ARIMA modeling process is model diagnostics. This involves evaluating whether the model assumptions are satisfied, whether the residuals are white noise, and whether the model is adequately fit to the data. You should learn various diagnostic plots to evaluate the model's performance, such as residuals plot, ACF plot, and QQ-plot.
AR model: Auto-Regression model considers the relationship between the dependent variable and its own lagged values. It involves predicting the present based on past values.
MA model: Moving Average model considers the relationship between the dependent variable and error terms as a moving average of p past errors.
ARMA model: Auto-Regressive Moving Average model combines both AR and MA models. It is a time series model that consists of two parts: The Autoregressive (AR) part and the Moving Average (MA) part.
ARIMA model: Auto-Regressive Integrated Moving Average model combines AR, MA models, and Integration. Integration is the ability to remove any stationary patterns from the input series.
SARIMA model: Seasonal Auto-Regressive Integrated Moving Average model is an extension of the ARIMA model that incorporates seasonality of a series.
SARIMAX model: Seasonal Auto-Regressive Integrated Moving Average with Exogenous Variables model is an extension of the SARIMA model that incorporates exogenous variables that influence the time series.
VAR model: Vector Auto-Regression model is used when several time series are involved which are interrelated.
VECM model: Vector Error Correction Model is used when the Vector Autoregression (VAR) model has non-stationary variables.
ARCH model: Autoregressive Conditional Heteroskedasticity model is used to model time-varying volatility in financial markets data.
GARCH model: Generalized Autoregressive Conditional Heteroskedasticity model is an extension of the ARCH model.
EGARCH model: Exponential Generalized Autoregressive Conditional Heteroskedasticity model is an extension of the GARCH model with asymmetric shocks.
TGARCH model: Threshold Generalized Autoregressive Conditional Heteroskedasticity model is used in financial time series where the unobserved volatility can shift regimes.
"ARIMA models are applied in some cases where data show evidence of non-stationarity in the sense of mean (but not variance/autocovariance)."
"an initial differencing step (corresponding to the 'integrated' part of the model) can be applied one or more times to eliminate the non-stationarity of the mean function (i.e., the trend)."
"When the seasonality shows in a time series, the seasonal-differencing could be applied to eliminate the seasonal component."
"we are motivated to make stationary a non-stationary time series, e.g., by using differencing, before we can use the ARMA model."
"the ARMA model, according to the Wold's decomposition theorem, is theoretically sufficient to describe a regular (a.k.a. purely nondeterministic) wide-sense stationary time series"
"The AR part of ARIMA indicates that the evolving variable of interest is regressed on its own lagged (i.e., prior) values."
"The MA part indicates that the regression error is actually a linear combination of error terms whose values occurred contemporaneously and at various times in the past."
"The I (for 'integrated') indicates that the data values have been replaced with the difference between their values and the previous values."
"The purpose of each of these features is to make the model fit the data as well as possible."
"Non-seasonal ARIMA models are generally denoted ARIMA(p,d,q) where parameters p, d, and q are non-negative integers."
"p is the order (number of time lags) of the autoregressive model."
"d is the degree of differencing (the number of times the data have had past values subtracted)."
"q is the order of the moving-average model."
"Seasonal ARIMA models are usually denoted ARIMA(p,d,q)(P,D,Q)m"
"where m refers to the number of periods in each season."
"the model may be referred to based on the non-zero parameter, dropping 'AR', 'I' or 'MA' from the acronym describing the model."
"ARIMA(1,0,0) is AR(1)."
"ARIMA(0,1,0) is I(1)."
"ARIMA(0,0,1) is MA(1)."