9. Predictive analytics

Question 1

Long-term forecasts

Answer 1

• one to five years
• Used for deciding whether:
  a new item should be put on the market
  an old one should be withdraw

Question 2

Medium-term forecasts

Answer 2

• a few months to one year
• Used for tactical logistical decisions, such as:
  Setting annual production and distribution plans
  Inventory management
  Slot allocation in warehouses

Question 3

Short-term forecasts

Answer 3

• a few days to several weeks
• Employed to schedule and reschedule resources in order to meet medium-term production and distribution targets

Question 4

Qualitative forecasting methods

Answer 4

• Based on expert judgement or on experimental approaches
• They can also make use of simple mathematical tools to combine different forecasts
• Usually employed for long- and medium-term forecasts when there are not enough data to use a quantitative approach

Question 5

Management judgement

Answer 5

• developed by the workforce (company management or sales force)
• Management knows a lot about the company business, including shifts in customers’ behaviour and the profile of prospective customers

Question 6

Delphi method

Answer 6

• A series of questionnaires is submitted to a panel of experts
• Every time a group of questions is answered, new sets of information become available
• A new questionnaire is prepared by a coordinator such that every expert is faced with the new findings
• Termination as soon as all experts share the same viewpoint
• Mainly used to estimate the influence of political, macro-economical changes on data patterns

Question 7

Market research

Answer 7

• Based on interviews with potential consumers or users
• Time consuming
• Deep knowledge of sampling theory
• Used only occasionally (when deciding whether a new product should be launched)

Question 8

Fig. Features of qualitative forecasting methods

Answer 8

Question 9

Quantitative forecasting methods

Answer 9

• Used every time there are enough data
• y_t, t = 1, . . . , T: sequence of the T past observations of the variable to be forecast, arranged according to the time of their outcome (time series or historical data)
• All the periods are equally spaced in time

Question 10

Continuous time series

Answer 10

low density index (usually < 30%)

Question 11

Sporadic time series

Answer 11

significant proportion (usually more than 30%) of zero values (ex. products with low demand)

Question 12

components of regular time series

Answer 12

Trend
Cyclical variation
Seasonal variation
Residual variation

Question 13

Trend

Answer 13

• Long-term modification of data patterns over time
• It may depend on changes in population and on the product (or service) life cycle

Question 14

Cyclical variation

Answer 14

• Caused by the “business cycle”, which depends on macro-economic issues
• Quite irregular, but its pattern is roughly periodic.

Question 15

Seasonal variation

Answer 15

• Caused by the periodicity of several human (ex. ups and downs in demand over the year) activities.
• Effect observed on a weekly horizon (some product sales higher on weekends than on working days)

Question 16

Residual variation

Answer 16

• Portion of the data pattern that cannot be interpreted as trend, cyclical or seasonal variation
• Result of numerous causes, each of which has a small impact.

Question 17

Forecasting process

Answer 17

1 Data preprocessing
2 Choice of the forecasting method
3 Evaluation of the forecasting accuracy

Question 18

rule of thumb to detect outliers

Answer 18

(In case of constant trend and no seasonal effect)
1 The first and third quartiles, Q_1 and Q_3, respectively, of the time series are identified
2 Data entries outside the interval [Q_1 − 1.5(Q_3 − Q_1), Q_3 + 1.5(Q_3 − Q_1)] are tagged as outliers
→ Idea: entries less than Q_1 − 1.5(Q_3 − Q_1), or greater than Q_3 + 1.5(Q_3 − Q_1), deviate

Question 19

Coefficient of variation of Y

Answer 19

relative dispersion of Y around the mean µ_Y , assuming µ_X > 0

Question 20

Removing the calendar variations

Answer 20

contain calendar effects (variable month length, day-of-the-week effects, holidays)
Replace each past observation y_t, t = 1, . . . , T, with the adjusted y´_t = w_t*y_t

Question 21

Deflating monetary time series

Answer 21

y´_t = y_t/w_t

Question 22

Adjusting for population variations

Answer 22

y´_t = y_t/w_t
w_t = a_t/a_1, t = 1, . . . , T
a_t: reference population in time period t, t = 1, . . . , T

Question 23

Normalizing the data

Answer 23

Linear interpolation

Question 24

pt(τ)

Answer 24

τ periods ahead forecast, made at time period t

Question 25

Error

Answer 25

(once parameter y_t becomes known at time t)
e_i(τ) = y_t − p_i(τ), i + τ = t

Question 26

Time series extrapolation methods, constant trend: Elementary technique

Answer 26

p_T+1 = yT

Question 27

Time series extrapolation methods, constant trend: Simple moving average method

Answer 27

Choice of r:
- small value: allows a rapid adjustment of the forecast to data pattern fluctuations and increases the influence of residual variations
- high value: filters the residual variations and produces a slow adaptation to data pattern variations

Question 28

Time series extrapolation methods, constant trend: Weighted moving average method

Answer 28

• Variation of the simple moving average method
• Lower weights are assigned to older data

Question 29

Time series extrapolation methods, constant trend: Exponential smoothing method (Brown method)

Answer 29

α ∈ [0, 1]: smoothing constant
Large value:
- A greater weight for more recent historical data
- A more outstanding capacity to follow the changes of values rapidly
- Less filtering of the residual variations of the time series
Low value: - A forecast less subject to random components
- The most recent data variations progressively available are incorporated in the forecast with a longer delay.

Question 30

Time series extrapolation methods, linear trend: Elementary technique

Answer 30

Question 31

Time series extrapolation methods, linear trend: Holt method

Answer 31

a1 = y1
b1 = 0

Question 32

Time series extrapolation methods, seasonal variation: Elementary technique

Answer 32

Question 33

Time series extrapolation methods, seasonal variation: Winters method

Answer 33

k: cycles
M: length of the cycle (in periods)