Lecture 4 - Time Series Forecasting Flashcards
Define time series forecasting
- 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
What ways can you identify characteristics in time series data
- 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
Define a time plot
*how can this help in selecting an appropriate time series forecasting approach?
depicts the overall trend of the data points across the entire time period.
- identify trends
Define a seasonal plot
*how can this help in selecting an appropriate time series forecasting approach?
revealing recurring patterns within the data that occur over specific time intervals (seasons)
*recognise seasonality patterns
Steps of time series forecasting
- Determine time horizon
- Gather and analyse data
*Select and validate forecasting model to use
- Make forecast
- Monitor and control forecast
What is a stationary series
- 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
What forecasting approaches are used for stationary series
- Simple Moving Average
- Exponential Smoothing
Key points about simple moving average
- 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
For a 3 week simple moving average, where does the first moving average point go
In the ‘3 week moving average’ column, in line with the 4th week’s data
Define bias in time series forecasting
a forecast is biased if they consistently overestimate or underestimate values
Why is average error not a good measurement of forecast accuracy (error and bias)
Because negative and positive errors will cancel out
Errors made consistently in one direction imply ….. what?
bias
Three common measures of TIME SERIES forecast accuracy
*Mean Absolute Deviation (MAD)
*Mean Squared Deviation/Error (MSD / MSE)
*Mean Absolute Percentage Error (MAPE)
What is MAD
*Mean Absolute Deviation
*measures the average of the absolute differences between forecasted values and actual values
How is ‘Mean Absolute Deviation’ calculated
𝗠𝗔𝗗 = Σ | 𝗙𝗼𝗿𝗲𝗰𝗮𝘀𝘁 - 𝗔𝗰𝘁𝘂𝗮𝗹 | / 𝗻
with Σ (sigma) representing the sum over all n data points.
&
|…| representing absolute value
Strengths and weaknesses of MAD as a metric to measure error and bias
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)
What is MSD/MSE
*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
How is ‘Mean Squared Deviation/Error’ calculated
Σ (Forecast - Actual)² / n
Strengths and weaknesses of MSD/MSE
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
What is MAPE
- Mean Absolute Percentage Error
- measures the average of the absolute percentage errors
How is ‘Mean Absolute Percentage Error’ calculated
Σ | (Forecast - Actual) / Actual | x 100% / n
Strengths and Weaknesses of MAPE
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
What is exponential smoothing
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.
A higher α (closer to 1) …..?
*less weight on past observations
*more responsive curve to changes in data
A lower α (closer to 0) …..?
*more weight on historical data
*more smooth curve, less sensitive to changes in data
Strengths and weaknesses of exponential smoothing
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
for practical reasons, what’s the best smoothing factor to use
(0.3 - 0.1)
because provides a stable series
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?
*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
Approaches to use when time series has a trend
and when the time series has a seasonality factor
TREND
*Trend extrapolation (linear regression)
- Holt’s method (double exponential smoothing)
SEASONALITY
* De-seasonalise
- Holt-Winters Technique (triple exponential smoothing)
Describe how to perform trend extrapolation (linear regression)
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
Describe Holt’s Method
(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
How to de-seasonalise a time series with a seasonality factor
- 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
Describe Holt-Winter’s technique
(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)
Some key further difficulties with time series forecasting
badly behaved series don’t allow for accurate forecasts
*Intermittent and erratic demand
What is forecast automation in time series forecasting
the use of software and tools to automate the process of generating forecasts for future values in a time series
Why is forecast automation important for companies that deal with many SKUs (Stock Keeping Units)?
any challenges?
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
