Time series involves analyzing data that evolves over some period of time and then utilizing statistical models to make predictions about future patterns and trends in the data.
Characteristics of time series data
Temporal Ordering - Time series data is ordered chronologically, with each observation occurring after the previous one. This ordering is essential for analyzing trends and patterns.
Time Dependency - In a time series, each observation is influenced by the preceding observations, creating a sequential relationship where the value at a given time depends on the values that occurred before it.
Irregular Sampling - Analyzing and forecasting time series data can be challenging when there are irregular or uneven time intervals between observations. Dealing with missing or irregularly spaced data points necessitates the use of suitable techniques.
Components of time series
Trend - This represents the long-term direction or tendency of the data. It captures the overall upward or downward movement over time. Trends can be linear (constant increase or decrease) or nonlinear (curved or oscillating).
Seasonality - Refers to patterns that repeat at fixed intervals within a time series. These patterns can be daily, weekly, monthly, or yearly. External factors such as weather conditions, holidays, or economic cycles often have an impact on seasonality.
Noise(random fluctuations/ irregularities) - Represents the unpredictable and random variations in the data and includes factors that cannot be explained by trend or seasonality. Measurement errors, random events, or unidentified factors can contribute to the presence of noise in the data.
Commonly used time series models
Moving Average (MA) Model - This model calculates the average of past observations with the aim of predicting future values. It is useful for capturing short-term fluctuations and random variations in the data.
Autoregressive (AR) Model - This model predicts future values based on a linear combination of past observations.
Autoregressive Moving Average (ARMA) Model - The ARMA model combines the AR and MA models to capture both short-term and long-term patterns in the data. It is effective for analyzing stationary time series data.
Autoregressive Integrated Moving Average (ARIMA) Model - This model extends the ARMA model by incorporating differencing to handle non-stationary data. It is suitable for data with trends or seasonality.
Seasonal ARIMA (SARIMA) Model - This model is an extension of the ARIMA model and includes seasonal components. It is useful for analyzing and forecasting data with recurring seasonal patterns.
Evaluating the performance of time series models.
Some commonly used metrics include:
Mean Absolute Error (MAE) - This metric measures the average absolute difference between the predicted and actual values. It provides a straightforward measure of the model’s accuracy.
Root Mean Squared Error (RMSE) - RMSE calculates the square root of the average squared difference between the predicted and actual values. It penalizes larger errors more heavily than MAE.
Mean Absolute Percentage Error (MAPE) - MAPE calculates the average percentage difference between the predicted and actual values. It provides a relative measure of the model’s accuracy.
Forecast Bias - Forecast bias measures the tendency of the model to consistently overestimate or underestimate the actual values. A bias close to zero indicates a well-calibrated model.
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