Time Series: Set of Observations Taken Sequentially over Time

Types of time series

• Regular time series: observations coming in at regular intervals of time
• Irregular time series: do not have observations at a regular interval of time

Main Areas of Application

• Time series forecasting: predicting the future values of a time series, when past values are given
• Time series classification: predict an action based on past values
• Interpretation and causality: understand the interrelationships among several related time series

Data-Generating Process (DGP)

• Generating synthetic time series: generate time series using a set of fundamental building blocks
  • White noise: an extreme case of a stochastic process, a sequence of random numbers with zero mean and constant standard deviation
  • Red noise: a sequence of random numbers with zero mean and constant variance but is serially correlated in time
  • Cyclical or seasonal signals: most common signals
  • Autoregressive signals: popular signal in the real world, outlined as follows;
    • number of previous timesteps the signal is dependent on
    • coefficients to combine the previous timesteps
  • Mix and match: using different components to make DGP to create time series
• Stationary time series: probability distribution remains the same at every point in time
• Non-stationary time series: most real world data, when stationary assumption broken, have two ways to verify this;
  • Change in mean over time: mean across two windows of time would not be the same
  • Change in variance over time: variance keeps getting bigger and bigger with time, means Heteroscedasticity

Predictability: three main factors to create a predictive model

• Understanding the DGP: better understanding of the DGP, higher the predictability
• Amount of data: more data, better predictability
• Adequately repeating pattern: more repeatable the pattern, better predictability

Forecasting Terminology

• Forecasting: prediction of future values of a time series using the known past values of the time series
• Multivariate forecasting: multivariate time series is not only dependent on its past values but also has some dependency on the other variables. Multivariate forecasting is a model that captures the interrelationship between the different variables along with its relationship with its past and forecast all the time series together in the future
• Explanatory forecasting: uses information other than its own history
• Backtesting: using the history to evaluate a trained model
• In-sample and out-sample: in-sample referring to metrics calculated on training data, and out-sample referring to metrics calculated on testing data
• Exogenous variables: not affected by other variables, help to create the model for the target outcome
• Endogenous variables: target variable, entirely dependent on other variables
• Forecast combination: combine multiple forecasts