[TBD]Machine learning business forecasting ISIBang

Terminology

Forecast - Estimate the some future event(s)

Time series - Chronological sequence of observations

Stationary series - Series which only shows random pattern. It means it will exhibit same statistical properties for any time-range (mean, median, standard deviation). If a series has external factor, then the series can't be stationary until external factors are removed

Auto-correlation -> Relation of the variable with itself by time shifting values

Classification

Short time forecast - For day, week or month

Medium time forecast - for one or two years range

Long time forecast - involves multiple years into future

Application

Operations management - Forecasting product sales
Marketing - Forecasting of sales response to advertisement
Finance and Risk managment
Process control -
Demography - Forecasting population by country

Methodology

Based on identifying, modelling and extrapolating the patterns found in historical data

Forecasting techniques

Quantitative method
1. Make use of historical data and forecasting model
2. Model summarizes pattern in data and establishes statistical relationship between past and current values
3. model is then used to project the patterns in the data into future
4. Forecasting model is used to extrapolate the past and current behaviour into the future
Qualitative method -
1. Properties
  1. Requires judgement of the expert
  2. Subjective in nature
2. Methods
  1. Delphi method
    1. Set of experts not sitting together will forecast. Their opinion will be combined and refined and finally arrive to the forecast

Quantitative models

Regression model
1. Make use of one or more related predictor values with the variable of interest
Smoothing model
1. Uses simple function of previous observations to provide forecast of the variable of interest
  1. Single smoothing model
  2. Double smoothing model
  3. ...
General time series model
1. Employs the statistical properties of the historical data to specify a formal model and then estimate the unknown parameter (generally using least square method)
Dynamic regression - It makes use of past values and also correlation with other variables
1. Intervention model
  1. Understand that y is not only related to past values. It will also be related to external factors (e.g. govt policies like lockdown)
  2. Formula is c+ (phi1)*(yt-1)+ (phi2)*(yt-2)+..... + (theta1)*(et-1) + (theta2)*(et-2)+........+b1*x1+b2*x2....
    1. Here x1, x2 ... are external factors
  3. Steps
    1. Draw scatter plot for past values
    2. Check if the series is stationary or not
    3. Plot ACF and PACF for what??
    4. Develop model using auto ARIMA
      1. Select model minimizing AIC
    5. Fit the model
      1. X=status on example. Status is external factor
    6. Check model accuracy
      1. MSE check
      2. MAE check
      3. RMSE
      4. Mean absolute percent error
    7. Draw actual vs predicted plot (scatter plot)
      1. to visually see if predicted values are good or not
  4. Dynamic regression
    1. It is extension of intervention model
    2. It makes use of past values and also correlation with other variables
    3. Steps
      1. Preliminary analysis
        No need to make series stationary
      2. Even though ACF and PACF doesn't show any info, we will go with auto-Arima
      3. Auto ARIMA is used for choosing best model
      4. Call fit with the best ARIMA model selected by auto-arima
      5. Plot ACF and PACF for normality test?
      6. Check errors
        MSE
        MAE
      7. Draw scatter plot for actual vs predicted
      8. Drop insignificant features
        Select feature which has p-value >0.05
      9. Retrain model with reduced feature set
Time series method
1. Exponential smoothing
2. ARIMA

Form of forecast

Point estimte or point forecast
1. A single value that represents the best estimate of the future value of the variable of interest
2. They are almost always wrong
Forecast error
1. Difference between predicted value and actual value
Prediction interval
1. A range of values for the future observation

Activities in forecasting process

Problem definition
Data collection
Preliminary data analysis
Model selection and fitting
Model validation
Forecast model deployment
Monitoring forecasting model performance
1. Ongoing activity after the deployment to ensure that the model is still performing satisfactorily

Exploration of time series data

It starts with time series plot.
Reveal patterns
1. Seasonal pattern
2. Trend
3. Level shifts
4. Cycles or Periods
5. Unusual observations

Preliminary data analysis

Plot and see
1. Use scatter plot for this (pyplot.scatter)
Check if series is stationary or not
1. Many statistical models works on stationary series
Convert series to stationary
1. Take diff of value with
  1. If trend, then diff with previous
  2. If seasonality, then diff with seasonility range
2. Keep repeating until we get the stationary series. Most cases, max 2 iteration is needed
3. Once we get the stationary series, then after go ahead creating the model

Detection of stationary series

By seeing the plot
By statistical test
1. ADF test
  1. Null hypothesis(H0) : mod(auto-correlation) = 1
    1. A small p-value(p<0.05) suggests that series is stationary
  2. If passes, it means it is not stationary. Otherwise it is stationary
2. KPSS test
  1. Test whether there is trend or not

Auto correlation

Shift the values by N unit, and then take correlation
Leg 1
1. Correlate by shifting with 1 unit
Leg 2
1. Correlate by shifting with 2 unit

Useful packages

Pandas
matplotlib.pyplot
statsmodel.tsa.stattools
statsmodel.??.holtwinters
probplot
plot_acf (acf - Auto Correlation Function), plot_pacf (pacf - Partial Auto correlation Function)
1. from statsmodel.graphics.tsaplots import plot_acf
statsmodels.tsa.arima_model
auto_arima
from pmdarima import auto_arima
from scipy import stats

Exponential smoothing types

Simple exponential smoothing
1. Have single parameter Alpha
2. Used for stationary
3. Alpha lies between 0 and 1
4. Alpha is estimated by minimizing the MSE
5. Give more weight to recent values compared to old values
6. Formula = Alpha * (previous actual value) + (1-Alpha)*(previous predicted value)
7. Forecast
  1. Point forecast
  2. Range forecast
    1. Formula - ??
8. Limitation
  1. We can predict only one value at a time
9. Steps
  1. Check if the series is stationary
  2. Use model to calculate alpha
  3. Predict by fitting the model
  4. Calculate residue (actual - predicted)
  5. Model error - Good model will have error<0.05 (5 %)
    1. Mean Square Error (MSE)
    2. Mean Absolute Error (MAE)
    3. Root Mean Square Error(R-MSE)
    4. Mean Absolute Percent Error - Mean(Absolute Error/actual value)
      1. <10% is reasonably good
  6. Model adequacy test
    1. Plot probplot over residue and check if it is normal distributed
  7. Model sufficiency
Double exponential smoothing
1. Have two parameters
2. Used for trend
Triple exponential smoothing
1. Have three parameters
2. Used for seasonal case

ARIMA (Auto regressive Integrated Moving Average)

Auto regressive -> Tells Correlation with how many past values

Moving average -> Tells Correlation with errors

More general ways to develop the forecasting model
1. Exponential smoothening can be the subclass of ARIMA
Series must be stationary??
Auto regressive meaning How many past values it is dependents on
Terms of ARIMA
1. How many past values(Phi1, Phi2....) it is dependents on? -> represented by p in ARIMA ..
2. How many error terms(Theta1, theta2.....) need to be added on? -> represented by q in ARIMA...
3. d ??
Auto ARIMA
1. Develop 20-25 models and select the one which gives minimum AIC or BIC (as per criteria)
Model diagnostic check
1. Errors or residual should be white noise and should not be auto correlated
  1. If p > 0.05, then there is no auto-correlation in residual
Partial correlation between X and Y

Reference