SARIMA

Time Series: A time series is a sequence of data points collected at regular intervals of time.

Stationarity: A stationary time series has constant statistical properties over time, such as mean and variance.

Autocorrelation: Autocorrelation refers to the correlation between a time series and its lagged values.

Seasonality: Seasonality is a regular pattern of data that repeats itself at a fixed interval. For example, the sales of ice cream tend to increase during the summer months.

SARIMA: Seasonal Autoregressive Integrated Moving Average (SARIMA) models are a class of time series models that allow for the modeling of both seasonality and trends.

ARIMA: Autoregressive Integrated Moving Average (ARIMA) models are a class of time series models used to analyze and forecast time series data. ARIMA models incorporate the dependencies among different lagged values of the time series.

Moving Average: A moving average is a method used to smooth out fluctuations in a time series by taking the average of a certain number of past observations.

Autoregression: Autoregression is a method of modeling time series data whereby the current value of the time series is modeled as a linear combination of past values.

Seasonal Decomposition: Seasonal decomposition is a method of extracting the seasonal, trend, and residual components of a time series.

Box-Jenkins Approach: The Box-Jenkins approach is a systematic method of model selection and parameter estimation for ARIMA models. The approach is based on the identification, estimation, and diagnostic testing of models.

Model Selection: Model selection is the process of choosing the best model among a set of candidate models based on some criteria, such as the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC).

Forecasting: Forecasting is the process of making predictions about future values of a time series based on its past behavior.

Error Metrics: Error metrics are used to measure the accuracy of the forecasting models. Examples of error metrics include Mean Absolute Error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE).

Cross-Validation: Cross-validation is a method of evaluating the performance of a forecasting model by fitting the model to a subset of the data and testing it on the remaining data.

Exponential Smoothing: Exponential smoothing is a method of forecasting time series data that assigns exponential weights to past observations.

As a language model AI, I do not have the capability to provide you an exhaustive list of all the different types of SARIMA (Time Series Analysis) along with a brief description of each type: However, I can provide a brief explanation of SARIMA.

SARIMA stands for Seasonal Autoregressive Integrated Moving Average: It is a class of models used for analyzing and forecasting time series data with seasonal components. This model is an extension of the ARIMA model, which is used for nonseasonal time series analysis. SARIMA models are designed to handle time series data that exhibits trends and seasonal patterns.

SARIMA models come in different orders, denoted by SARIMA(p, d, q)x(P, D, Q)[S]: Here's what each parameter means:.

p: The autoregressive order (AR) of the model. It is the number of lagged observations of the dependent variable that are included in the model.

d: The order of differencing (I) required to stationarize the time series. It is the number of times the series is differenced until it becomes stationary.

q: The moving average order (MA) of the model. It is the number of lagged forecast errors from the regression equation that are included in the model.

P, D, Q: The seasonal autoregressive order (SAR), the seasonal differencing order (SI), and the seasonal moving average order (SMA), respectively.

S: The number of periods in a season.

SARIMA models can be used for various applications, such as sales forecasting, weather forecasting, economic forecasting, and more.: SARIMA models in Economics are sophisticated time series models that can be utilized for forecasting future trends in variables like sales, weather patterns or economic indicators.