9. Predictive analytics Flashcards
Long-term forecasts
- one to five years
- Used for deciding whether:
a new item should be put on the market
an old one should be withdraw
Medium-term forecasts
- 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
Short-term forecasts
- a few days to several weeks
- Employed to schedule and reschedule resources in order to meet medium-term production and distribution targets
Qualitative forecasting methods
- 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
Management judgement
- 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
Delphi method
- 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
Market research
- 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)
Fig. Features of qualitative forecasting methods
Quantitative forecasting methods
- 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
Continuous time series
low density index (usually < 30%)
Sporadic time series
significant proportion (usually more than 30%) of zero values (ex. products with low demand)
components of regular time series
Trend
Cyclical variation
Seasonal variation
Residual variation
Trend
- Long-term modification of data patterns over time
- It may depend on changes in population and on the product (or service) life cycle
Cyclical variation
- Caused by the “business cycle”, which depends on macro-economic issues
- Quite irregular, but its pattern is roughly periodic.
Seasonal variation
- 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)
Residual variation
- 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.
Forecasting process
1 Data preprocessing
2 Choice of the forecasting method
3 Evaluation of the forecasting accuracy
rule of thumb to detect outliers
(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
Coefficient of variation of Y
relative dispersion of Y around the mean µ_Y , assuming µ_X > 0
Removing the calendar variations
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
Deflating monetary time series
y´_t = y_t/w_t
Adjusting for population variations
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
Normalizing the data
Linear interpolation
pt(τ)
τ periods ahead forecast, made at time period t
Error
(once parameter y_t becomes known at time t)
e_i(τ) = y_t − p_i(τ), i + τ = t
Time series extrapolation methods, constant trend: Elementary technique
p_T+1 = yT
Time series extrapolation methods, constant trend: Simple moving average method
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
Time series extrapolation methods, constant trend: Weighted moving average method
- Variation of the simple moving average method
- Lower weights are assigned to older data
Time series extrapolation methods, constant trend: Exponential smoothing method (Brown method)
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.
Time series extrapolation methods, linear trend: Elementary technique
Time series extrapolation methods, linear trend: Holt method
a1 = y1
b1 = 0
Time series extrapolation methods, seasonal variation: Elementary technique
Time series extrapolation methods, seasonal variation: Winters method
k: cycles
M: length of the cycle (in periods)
