Time-Series MLM

Question 1

Time-series analysis

Answer 1

Time-series analysis comprises methods for analyzing time-series data to extract meaningful statistics and other characteristics. Time-series forecasting is the use of a model to predict future values based on previously observed values.

Question 2

1. Autoregressive Integrated Moving Average (ARIMA)

Answer 2

ARIMA models capture a suite of different standard temporal structures in time series data. It is specified by three order parameters (p, d, q), where ‘p’ is the order of the Autoregressive part; ‘d’ is the order of differencing required for stationarity; and ‘q’ is the order of the Moving Average part.

Question 3

2. Seasonal Autoregressive Integrated Moving-Average (SARIMA)

Answer 3

An extension of ARIMA that explicitly supports univariate time series data with a seasonal component. It adds three new hyperparameters to specify the autoregression (AR), differencing (I), and moving average (MA) for the seasonal component of the series, as well as an additional parameter for the period of the seasonality.

Question 4

3. Vector Autoregression (VAR)

Answer 4

An extension of AR models that allows for the simultaneous modeling of multiple, interrelated time series variables, all of which are treated as endogenous. The structure captures the linear interdependencies among the variables.

Question 5

4. Prophet

Answer 5

Developed by Facebook, Prophet is designed for analyzing time-series that display patterns on different time scales such as yearly, weekly and daily. It also has advanced capabilities for modeling the effects of holidays on a time-series.

Question 6

5. Exponential Smoothing (ETS)

Answer 6

ETS models, such as Holt’s linear exponential smoothing, capture trend and seasonality in time series data. The Triple Exponential Smoothing (Holt-Winters method) can handle both trends and seasonality.

Question 7

6. Recurrent Neural Networks (RNN)

Answer 7

RNNs, specifically Long Short-Term Memory (LSTM) networks, have been used with a lot of success for time-series forecasting. LSTMs are able to remember important events or patterns in the past data and can use this information to influence the output for the current step.

Question 8

7. Gated Recurrent Unit (GRU)

Answer 8

Similar to LSTMs, GRUs are another type of recurrent neural network that have seen use in time-series analysis. They also have gating units, but with a slightly different and less complex internal structure.

Question 9

8. State Space Models

Answer 9

State Space Models and the Kalman filter can handle multiple structural components such as trends and seasonality, as well as the errors, in a unified framework.

Question 10

9. Gaussian Processes

Answer 10

Gaussian Processes are used for regression tasks. They are flexible and fully specified by a mean and a covariance function, making them especially useful for modelling time series data.