Time Series Analysis

Question 1

Time Series Analysis

Answer 1

A quantitative forecasting method to predict future value

Uses numerical data obtained at regular time intervals

projections based on past and present observation

Question 2

Components of time series analysis

Answer 2

trend, cycles, seasonal, and random factors

Question 3

Cyclical vs Seasonal

Answer 3

Regular patterns when looking at yearly increments

VS

upward and downward swings of varying lengths

Question 4

Random Component

Answer 4

-erratic, nonsystematic, random, or residual flucuations.

Short duration and non-repeating

Due to nature or accidents

Question 5

Univariate vs Multivariate Time Series Models

Answer 5

Univariate
Uses only one variable
Cannot use external data
Based only on relationships between past and present

Multivariate
Uses multiple variables
can use external data
based on relationships between past and present AND between variables

Question 6

Time Series Decomposition

Answer 6

A technique to extract multiple types of variation from your dataset.

There are 3 important components in the temporal data of a time series - seasonality, trend, and noise (can not be explained by either season or trend)

It results in a graph of each component

Question 7

Trend

Answer 7

a longterm upward or downward pattern in your data

Question 8

Autocorrelation

Answer 8

the correlation between a time series’ current value and its past value. If a correlation exists, you can use present values to better predict future values

Positive autocorrelation - a high value now is likely to yield a high value in the future and vise versa

Negative autocorrelation - an inverse relationship. A high value implies a low value tomorrow and vice versa. Think about population control via competition in the wild.

ACF = autocorrelation function

Question 9

PACF

Answer 9

An alternative to ACF. Rather than giving the autocorrelations, it gives you PARTIAL autocorrelations. It is partial because with each step back in the past, only additional autocorrelation is listed.

ACF contains duplicate correlations when variability can be explained by multiple points in time.

For example, if the value of today is the same as the value of yesterday, but also the same as the day before yesterday, AFC would show 2 highly correlated steps. PACF would only the yesterday’s correlation and will remove the ones further in the past

Question 10

Stationarity

Answer 10

A time series that has no trend. Some time series models are not able to deal with trends. You can detect non-stationarity using the dickey fuller test and you can remove non-stationarity using differencing

The mean and variance do not change over time!

Question 11

Dickey Fuller Test

Answer 11

ADF test

p value smaller than .05 - reject the null (non-stationarity) and accept the alternative (trend)

Question 12

Differencing

Answer 12

Removing the trend from your time series, the goal is to only have seasonal variation left.

This allows you to use models that can handle seasonality but not trend

Question 13

One Step Time Series models

Answer 13

Designed to forcast only one step into the future
Can generate multistep forecasts by windowing over predictions
can be less performant for multistep forecasts

Question 14

Multistep Forecasts

Answer 14

designed to forecast multiple steps into the future

no need to window over predictions

more appropriate for multistep forecasts

Question 15

Classical Time Series Models

Answer 15

These models are strongly based on temporal variation inside a time series and they work well with univariate time series

ARIMA Family falls in this category

Question 16

ARIMA Family

Answer 16

Autoregression (AR) - Uses a regression model that explains a variables future based on its past values. It only uses the value of the previous step to predict the current value

Moving Average (MA) - Same in concept as AR - uses past to predict future. BUT the past values used are not the value of the variables, rather it uses the prediction error in the previous steps to predict the future

Question 17

Autoregressive moving average (ARMA)

Answer 17

Combines both AR and MA into one. It uses both previous value and prediction errors from the past to predict the future.

Requires stationary data!! Must remove trend via differencing before using

Question 18

Autoregressive Integrated Moving Average

Answer 18

ARIMA adds auto differencing right into your model, so you can feed it non-stationary data

Question 19

Smoothing

Answer 19

smoothing is a basic statistical technique that can be used to smoothen out time series. Time series patterns often have a lot of long term variability but also short term variability (noise)

Smoothing reduces the short term variability so you can see the long term trends more easily

Question 20

Simple moving average

Answer 20

the simplest smoothing technique. It replaces current value and surrounding value with a very local average of a few pre and post values

Question 21

Simple Exponential smoothing

Answer 21

an adaptation of moving average. But rather than taking a simple average, it takes a weighted average (a value that is further back will count less and a more recent value will count more)

The weights are chosen subjectively

When trends are present (non-stationary) you should avoid using this technique.

Question 22

Double Exponential smoothing

Answer 22

You can use this for smoothing non-stationary data.