Lecture 4 - Time Series Forecasting

Question 1

Define time series forecasting

Answer 1

• technique that tries to predict how a sequence of historical data will continue in the future, by analysing the data and identifying patterns/trends in the series

Question 2

What ways can you identify characteristics in time series data

Answer 2

• visualisation
• identify patterns, possible explanations for variation in the data
• statistical analysis
• for time series –> time plot
• for seasonal time series –> seasonal plot

–> both can reveal trends, or seasonal behaviour

Question 3

Define a time plot

*how can this help in selecting an appropriate time series forecasting approach?

Answer 3

depicts the overall trend of the data points across the entire time period.

• identify trends

Question 4

Define a seasonal plot

*how can this help in selecting an appropriate time series forecasting approach?

Answer 4

revealing recurring patterns within the data that occur over specific time intervals (seasons)

*recognise seasonality patterns

Question 5

Steps of time series forecasting

Answer 5

• Determine time horizon
• Gather and analyse data

*Select and validate forecasting model to use

• Make forecast
• Monitor and control forecast

Question 6

What is a stationary series

Answer 6

• a data sequence which has no strong trend or seasonal component
• we assume it is essentially constant over the long term with short term fluctuations

Question 7

What forecasting approaches are used for stationary series

Answer 7

• Simple Moving Average
• Exponential Smoothing

Question 8

Key points about simple moving average

Answer 8

• Only user input choice is the length of the moving average

–> short average provides more response to changing demand levels, but may not be desirable

–> long average provides more smoothing, but may miss trends and turning points

Question 9

For a 3 week simple moving average, where does the first moving average point go

Answer 9

In the ‘3 week moving average’ column, in line with the 4th week’s data

Question 10

Define bias in time series forecasting

Answer 10

a forecast is biased if they consistently overestimate or underestimate values

Question 11

Why is average error not a good measurement of forecast accuracy (error and bias)

Answer 11

Because negative and positive errors will cancel out

Question 12

Errors made consistently in one direction imply ….. what?

Answer 12

bias

Question 13

Three common measures of TIME SERIES forecast accuracy

Answer 13

*Mean Absolute Deviation (MAD)

*Mean Squared Deviation/Error (MSD / MSE)

*Mean Absolute Percentage Error (MAPE)

Question 14

What is MAD

Answer 14

*Mean Absolute Deviation

*measures the average of the absolute differences between forecasted values and actual values

Question 15

How is ‘Mean Absolute Deviation’ calculated

Answer 15

𝗠𝗔𝗗 = Σ | 𝗙𝗼𝗿𝗲𝗰𝗮𝘀𝘁 - 𝗔𝗰𝘁𝘂𝗮𝗹 | / 𝗻

with Σ (sigma) representing the sum over all n data points.

&

|…| representing absolute value

Question 16

Strengths and weaknesses of MAD as a metric to measure error and bias

Answer 16

Strength
* easy to interpret as in sameΣ | (Forecast - Actual) / Actual | * 100% / n scale with the data
* less sensitive to outliers than MSE

Weakness
*doesn’t consider magnitude of errors (as mean treats all errors equally)

Question 17

What is MSD/MSE

Answer 17

*Mean Squared Deviation/Error

*measures the average of the squared differences between the forecasted values and the actual values

• squaring the differences gives more weight to larger errors

Question 18

How is ‘Mean Squared Deviation/Error’ calculated

Answer 18

Σ (Forecast - Actual)² / n

Question 19

Strengths and weaknesses of MSD/MSE

Answer 19

Strengths
*more sensitive to larger errors (due to squaring)

Weaknesses
* results can be skewed by outliers
*can be difficult to interpret error without converting back to original scale of data

Question 20

What is MAPE

Answer 20

• Mean Absolute Percentage Error
• measures the average of the absolute percentage errors

Question 21

How is ‘Mean Absolute Percentage Error’ calculated

Answer 21

Σ | (Forecast - Actual) / Actual | x 100% / n

Question 22

Strengths and Weaknesses of MAPE

Answer 22

Strengths
*easily interpreted as a %
–> therefore useful for comparison across data sets 𝘄𝗶𝘁𝗵 𝗱𝗶𝗳𝗳𝗲𝗿𝗲𝗻𝘁 𝘀𝗰𝗮𝗹𝗲𝘀.

Weaknesses
* can be misleading when demand levels are very low (close to 0 would mean dividing by 0’s)
* sensitive to outliers

Question 23

What is exponential smoothing

Answer 23

forecasting technique that assigns exponentially decreasing weights to past observations when generating forecasts

• assigns higher weights to more recent data points and lower weights to older ones, therefore giving them less influence on the forecast.

Question 24

A higher α (closer to 1) …..?

Answer 24

*less weight on past observations

*more responsive curve to changes in data

Question 25

A lower α (closer to 0) …..?

Answer 25

*more weight on historical data

*more smooth curve, less sensitive to changes in data

Question 26

Strengths and weaknesses of exponential smoothing

Answer 26

Strengths
* practical forecasting method –> easy to use

*focus on recent data and current situation

Weaknesses
*difficulty handling complex data with multiple trends/relationships

*subjective selection of smoothing factor (may require experimentation to find best parameter –> time consuming)

*lags behind trends, if one is present

Question 27

for practical reasons, what’s the best smoothing factor to use

Answer 27

(0.3 - 0.1)

because provides a stable series

Question 28

Why§ Why is it not a good idea to use (simple) exponential smoothing or moving averages for a time series with a significant trend effect?

Answer 28

*struggle to capture trends as the importance of older data points decreases over time
–> these points may hold important information regarding the trend

*both gradually converge to a constant value
–> predicting that the pattern in the series will eventually flatten out

*weighting makes it slow to react to significant changes in trend

Question 29

Approaches to use when time series has a trend

and when the time series has a seasonality factor

Answer 29

TREND
*Trend extrapolation (linear regression)

• Holt’s method (double exponential smoothing)

SEASONALITY
* De-seasonalise

• Holt-Winters Technique (triple exponential smoothing)

Question 30

Describe how to perform trend extrapolation (linear regression)

Answer 30

find the line of best fit (need to know intercept and slope)

y = mx + c

least square method
- sum of vertical distances between predicted and actual demand , all squared

Question 31

Describe Holt’s Method

Answer 31

(for linear trends)

• exponential smoothing with two smoothing factors
  –> one focus on smoothing the base (intercept) with weighting the most recent observation like in exp. smoothing

–> second focus on the trend (slope) based on the difference between most recent forecast and previous level estimate

Question 32

How to de-seasonalise a time series with a seasonality factor

Answer 32

• calculate sample mean of all values

*divide each observation by sample mean, to find initial seasonal factors

• average the factors for like periods (e.g. mean of all mondays, mean of all tuesdays and so on)
• this finds the seasonal factors

*FORECAST (e.g. forecast for Tuesdays)
- sample mean x seasonal factor for Tuesdays

Question 33

Describe Holt-Winter’s technique

Answer 33

(triple exponential smoothing)

‘De-trend’ and ‘de-seasonalise’ the time series by separating base from trend and seasonality effects

• base (intercept) smoothing
• trend (slope) smoothing

*seasonal smoothing (with seasonal co-efficient)

Question 34

Some key further difficulties with time series forecasting

Answer 34

badly behaved series don’t allow for accurate forecasts

*Intermittent and erratic demand

Question 35

What is forecast automation in time series forecasting

Answer 35

the use of software and tools to automate the process of generating forecasts for future values in a time series

Question 36

Why is forecast automation important for companies that deal with many SKUs (Stock Keeping Units)?

any challenges?

Answer 36

𝗜𝗺𝗽𝗼𝗿𝘁𝗮𝗻𝘁 𝗕𝗲𝗰𝗮𝘂𝘀𝗲..

• more efficient and accurate as less manual intervention
• scalable
• can update easily with new trends or data
• consistent across all stock units
  *data driven insights can inform pricing and marketing strategies

𝗖𝗵𝗮𝗹𝗹𝗲𝗻𝗴𝗲𝘀…

• human judgement required to adjust forecasts because of internal (price changes, promotions) or external factors (economy, actions of competition)
  –> also outlier spotting is done by humans