TSA

The statistical properties are the same at any point in time.

Many TSA models, like ARIMA, assume the data is stationary. If not, the models may not work properly.

Used to model relationships between time series data and predictors.

Methods for analyzing time-ordered data to extract meaningful statistics and patterns.

A better model fit in forecasting accuracy.

Subtracting consecutive values to make the data stationary.

A type of regression where past values of the series are used as predictors.

A time series model that expresses the output as a linear combination of past forecast errors.

Applying mathematical functions (e.g., log, square root) to stabilize variance.

Estimating future data points based on past observations without future data influencing the estimate.

A series of data points indexed in time order (e.g., stock prices, weather data, etc.).

Mean and variance are constant, and autocovariance only depends on the time difference.

Y_t = μ + ε_t + θ_1 ε_{t-1} + θ_2 ε_{t-2} + ... + θ_q ε_{t-q}

A stationary time series has constant mean, variance, and autocovariance over time.

MSE = (1/n) ∑(Y_i - ŷ_i)²

Finance (predicting stock prices), Weather Forecasting (analyzing temperature patterns), Economics (studying GDP growth), Engineering (monitoring system performance), Medicine (tracking disease outbreak data).

Removing long-term trends from the data to achieve stationarity.

A measure of the average of the squares of the errors between actual values and predicted values.