forecasting model
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This document provides an overview and examples of forecasting models, including: - Random walk models for time series prediction where each value is determined by the previous value plus some random variation. Autocorrelation decreases with lag for random walks. - Hidden Markov models for stock prediction where an unseen ("hidden") process generates observable outputs. The probabilities of state transitions and emissions can be estimated from visible data. - Multi-variable time series prediction using WEKA, including loading and preprocessing sales data, configuring periodic attributes, and evaluating models like linear regression. Accuracy can be improved by optimizing algorithms, data, and features.
![What is the forecasting
• Correlation
• Time series data can be analyzed and evaluated from the past few data to see
the correlation, such as measuring the relationship between Xt, Xt-1, Xt-2, …Xt-n
• Indicates the degree of correlation between time series data and previous data,
Autocorrelation function (ACF) can be used to determine whether this time
series data has stationarity or seasonality or periodicity properties.
• ACF value between [-1,1], 1: Positive correlation, -1: Negative correlation, 0: Not
relevant.
13
ACF value by lag0~lag24 with higher than statistically significant (fixed value),
It means the series is non-stationary
Fixed value](https://image.slidesharecdn.com/3forecastingmodel-210603100141/85/forecasting-model-13-320.jpg)
![Random Walk for Time-Series
• Random Walk and Stationarity (ADF)
• A stationary time series is one where the values are NOT a function of time.
• Use Augmented Dickey-Fuller test (ADF). Range: [-1,1] => Most positive/ negative
series autocorrelation; 0: non-autocorrelation
• Predicting a Random Walk
• A random walk is unpredictable; it cannot reasonably be predicted.
• Make a stationary Random Walk Time-Series
• Difference (Lag).
• All correlations are small, close to zero.
random_walk_demo.ipynb
predicting_a_random_walk.ipynb
18](https://image.slidesharecdn.com/3forecastingmodel-210603100141/85/forecasting-model-18-320.jpg)
![Hidden Markov Model for stock prediction
• Definition
• Roll the dice 10 times, the series are [1 6 3 5 2 7 3 5 2 4] => 「Visible status chain」
• Invisible status chain may be from those dices [D6 D8 D8 D6 D4 D8 D6 D6 D4 D8]
• Visible status
• Status emission probability
• Invisible status
• Status transition probability, it is a HMM
21
Human: Status chain
Computer: Transition probability](https://image.slidesharecdn.com/3forecastingmodel-210603100141/85/forecasting-model-21-320.jpg)
![Hidden Markov Model for stock prediction
• Find the probability
• Visible state are in series [1 6 3 5 2 7 3 5 2 4]
24
P1(D4) => 1/4
P2(D6) = P1(D4)*P(D4 to 1)*P(D4 to D6)*P(D6 to 6) => 1/3* 1/4* 1/3* 1/6
P3(D4) = P2(D6)*P(D6 to D4)*P(D4 to 3) => 1/216 * 1/3 * 1/4
1 point with the highest probability to dice D4
Three types of dice we have
• D4
• D6
• D8](https://image.slidesharecdn.com/3forecastingmodel-210603100141/85/forecasting-model-24-320.jpg)
![Hidden Markov Model for stock prediction
• How to calculate the most probability of invisible state
• Brute force (for each result of all combination, p21~p23)
• Viterbi algorithm (make a hidden status chain from visible states)
28
x: hidden status
y: visible status
a: transition probabilities
b: emission probabilities
Dice: X2, X1, X3
Homework1: Continue to the visible series of dice [1 6 3 5 2 7 3 5 2 4], P4 ~ P10](https://image.slidesharecdn.com/3forecastingmodel-210603100141/85/forecasting-model-28-320.jpg)
![Homework
• Calculate the invisible states from visible series of dice [1 6 3 5 2 7 3 5
2 4]
• Continue to improve performance in WEKA sales order prediction
• Change algorithms
• Add more observation data
• If we don’t use Periodic attributes or Overlay data
45](https://image.slidesharecdn.com/3forecastingmodel-210603100141/85/forecasting-model-45-320.jpg)
forecasting model
- 1. 國立臺北護理健康大學 NTUHS Forecasting Model Orozco Hsu 2021-05-20 1
- 2. About me • Education • NCU (MIS)、NCCU (CS) • Work Experience • Telecom big data Innovation • AI projects • Retail marketing technology • User Group • TW Spark User Group • TW Hadoop User Group • Taiwan Data Engineer Association Director • Research • Big Data/ ML/ AIOT/ AI Columnist 2 「How can you not get romantic about baseball ? 」
- 3. Tutorial Content 3 What is the forecasting Random Walk for Time-Series Hidden Markov Model for stock prediction Homework Multi-variables or Periodic attributes Time-Series prediction (WEKA)
- 4. Code • Download code • https://github.com/orozcohsu/ntunhs_2020/tree/master/alg_20210520 4
- 5. What is the forecasting 5
- 6. What is the forecasting • Key Terms and differences Forecasting Predictive Modeling 6
- 7. What is the forecasting • Forecasting is a process of predicting or estimating the future based on past and present data. • Examples: • How many passengers can we expect in a given flight? • How many customer calls can we expect in next hour? (Poisson distribution) • Weather forecasting • Stock market forecasting 7
- 8. What is the forecasting • Passengers count forecasting for next one year Time series 8
- 9. What is the forecasting • Predictive modeling, used to perform prediction more granular. • Complex variable test • Data sampling • Feature selection • Data visualization • Examples: • Who are the customers who are likely to buy a product in next month? • And then taking action accordingly. 9
- 10. What is the forecasting • Some useful tools • Moving average forecasting (MA) • Simple Exponential Smoothing forecasting(SES; Holt-Winters seasonal method) • Stepwise Autoregressive forecasting • Autoregressive Integrated Moving Average model forecasting (ARIMA) • Autoregressive conditional heteroskedasticity forecasting (ARCH) • Value at Risk • Hidden Markov Model forecasting (HMM) • Multi-variables or Periodic attributes Time-Series forecasting 10
- 11. What is the forecasting • Random or non-random series • Yes, it’s a random series, so we can’t forecast it anything. • No, it’s a non-random series, but it’s chaotic time series. The purpose of chaos theory is to reveal the simple laws that may be hidden behind seemingly random series. 11 It’s a real mess. It looks nothing like a time series. It also NOT a random walk series. Chaotic time series: it looks like the random series, but it generates from a specific function behind. Refer to chaotic time series analysis. Question: A series of random number were generated by computer (seed), is that a RANDOM OR NON-RANDOM?
- 12. What is the forecasting • Stationary or non-stationary series • An assumption must be made that our observations all come from the same distribution function, it is called stationary. • Indicates that the standard deviation and/or average value of time series data will NOT change over time and it has a certain regularity. • Time series data will be stationary if seasonality and trend are removed. • From this point of view, we discuss correlation. 12
- 13. What is the forecasting • Correlation • Time series data can be analyzed and evaluated from the past few data to see the correlation, such as measuring the relationship between Xt, Xt-1, Xt-2, …Xt-n • Indicates the degree of correlation between time series data and previous data, Autocorrelation function (ACF) can be used to determine whether this time series data has stationarity or seasonality or periodicity properties. • ACF value between [-1,1], 1: Positive correlation, -1: Negative correlation, 0: Not relevant. 13 ACF value by lag0~lag24 with higher than statistically significant (fixed value), It means the series is non-stationary Fixed value
- 14. Random Walk for Time-Series 14
- 15. Random Walk for Time-Series • We know autocorrelation is closer to zero, it is a random walk series. • A random walk is unpredictable; it cannot reasonably be predicted. • Why? • Because we know that the next time step will be a function of the prior time step, highly relatived with time. • We called it as naive forecast, or a persistence model. • Many time series are random walks, particularly those of security prices over time. • The random walk hypothesis is a theory that stock market prices are a random walk and cannot be predicted. 15
- 16. Random Walk for Time-Series • A random walk is different from a list of random numbers because the next value in the sequence is a modification of the previous value in the sequence. • Start with a random number of either -1 or 1 • Randomly select a -1 or 1 and add it to the observation from the previous time step. • Repeat step 2 for as long as you like. • From step-to-step rather than the large jumps that a series of independent, random numbers provides. y(t) = B0 + B1*X(t-1) + e(t) White noise/ random function Observation at the previous time step Coefficient to weight 16 The next value in the series Coefficient
- 17. Random Walk for Time-Series • Random Walk and Autocorrelation • Calculate the correlation between each observation and the observations at previous time steps. • It is constructed, we would expect a strong autocorrelation with the previous observation and a linear fall off from there with previous lag values. 17 Lag Random walk is constructed, so the beginning of lag the autocorrelation value is high. (The current observation is a random step from the previous observation)
- 18. Random Walk for Time-Series • Random Walk and Stationarity (ADF) • A stationary time series is one where the values are NOT a function of time. • Use Augmented Dickey-Fuller test (ADF). Range: [-1,1] => Most positive/ negative series autocorrelation; 0: non-autocorrelation • Predicting a Random Walk • A random walk is unpredictable; it cannot reasonably be predicted. • Make a stationary Random Walk Time-Series • Difference (Lag). • All correlations are small, close to zero. random_walk_demo.ipynb predicting_a_random_walk.ipynb 18
- 19. Hidden Markov Model for stock prediction 19
- 20. Hidden Markov Model for stock prediction • A hidden process of unknown parameters. • The most difficult part is unknown parameters of observation. 20
- 21. Hidden Markov Model for stock prediction • Definition • Roll the dice 10 times, the series are [1 6 3 5 2 7 3 5 2 4] => 「Visible status chain」 • Invisible status chain may be from those dices [D6 D8 D8 D6 D4 D8 D6 D6 D4 D8] • Visible status • Status emission probability • Invisible status • Status transition probability, it is a HMM 21 Human: Status chain Computer: Transition probability
- 22. Hidden Markov Model for stock prediction • Question • Known types of dice, and transition probability • From visible status results to find the which of dice. • Knows types of dice, and transition probability • From visible status results to find the probability of dice. • Only known types of dice. • From visible status results to find the transition probability. 22
- 23. Hidden Markov Model for stock prediction • Find the probability • P = P(D6)*P(D6 to 1)*P(D6 to D8)*P(D8 to 6)*P(D8 to D8)*P(D8 to 3) • => 1/3 * 1/6 * 1/3 * 1/8 * 1/3 * 1/8 23
- 24. Hidden Markov Model for stock prediction • Find the probability • Visible state are in series [1 6 3 5 2 7 3 5 2 4] 24 P1(D4) => 1/4 P2(D6) = P1(D4)*P(D4 to 1)*P(D4 to D6)*P(D6 to 6) => 1/3* 1/4* 1/3* 1/6 P3(D4) = P2(D6)*P(D6 to D4)*P(D4 to 3) => 1/216 * 1/3 * 1/4 1 point with the highest probability to dice D4 Three types of dice we have • D4 • D6 • D8
- 25. Hidden Markov Model for stock prediction • Sum all of probabilities 25 We have 3 types of dice, and randomly pick one of dice and roll with 1 point. The probability is 18%
- 26. Hidden Markov Model for stock prediction • Sum all of probabilities 26
- 27. Hidden Markov Model for stock prediction • Sum all of probabilities 27
- 28. Hidden Markov Model for stock prediction • How to calculate the most probability of invisible state • Brute force (for each result of all combination, p21~p23) • Viterbi algorithm (make a hidden status chain from visible states) 28 x: hidden status y: visible status a: transition probabilities b: emission probabilities Dice: X2, X1, X3 Homework1: Continue to the visible series of dice [1 6 3 5 2 7 3 5 2 4], P4 ~ P10
- 29. Hidden Markov Model for stock prediction • FB market stock prediction (Using Markov property, not pure time series) • Download historical data from • https://www.nasdaq.com/market-activity/stocks/fb/historical 29 hmm_makrtket_stock_prediction.ipynb Stock data we used is not based on random walk time series data, check the code!
- 30. Hidden Markov Model for stock prediction • Extract feature 30
- 31. Multi-variables or Periodic attributes Time- Series prediction (WEKA) 31
- 32. Multi-variables or Periodic attributes Time- Series prediction (WEKA) • WEKA • The workbench for machine learning. • It is widely used for teaching, research, and industrial applications, contains a plethora of built-in tools for standard machine learning tasks, and additionally gives transparent access to well-known toolboxes such as scikit-learn, R. • WEKA Installation and import packages • Demo https://www.cs.waikato.ac.nz/ml/weka/ https://sourceforge.net/projects/weka/ 32
- 33. Multi-variables or Periodic attributes Time- Series prediction (WEKA) 33
- 34. Multi-variables or Periodic attributes Time- Series prediction (WEKA) 34
- 35. Multi-variables or Periodic attributes Time- Series prediction (WEKA) • Sales order prediction Observation Overlay data Row data remove or not • WEKA requires • Input data format must be ARFF • You need to convert your csv • Covert to WEKA ARFF format • https://pulipulichen.github.io/jieba- js/weka/spreadsheet2arff/index.html • Download the ARFF files 35
- 36. Multi-variables or Periodic attributes Time- Series prediction (WEKA) • Load Data • Find the ARFF file 36 4 columns
- 37. Multi-variables or Periodic attributes Time- Series prediction (WEKA) • Basic configuration • Number of time units forecast = 25 • Periodicity = Daily • Copy the content from skip_list- sales_order_1_8_p9.txt and paste it • Check Perform evaluation 37
- 38. Multi-variables or Periodic attributes Time- Series prediction (WEKA) • Base learner • LinearRegression • MultilayerPerceptron • SMOreg (SVM) 38 Homework2: Continue to improve performance in WEKA sales order prediction
- 39. Multi-variables or Periodic attributes Time- Series prediction (WEKA) • Click 「periodic attributes」 • Check Customize • Load file form periodics_set- sales_order_1_8_p9.periodics 39
- 40. Multi-variables or Periodic attributes Time- Series prediction (WEKA) • Output • Check Graph target at steps • Press Start button 40
- 41. Multi-variables or Periodic attributes Time- Series prediction (WEKA) • Output Prediction with asterisk 41 Using Linear Regression Model with those variables
- 42. Multi-variables or Periodic attributes Time- Series prediction (WEKA) • Output/ Prediction at steps 42 NOT so good, is it good using prediction model to forecast future value?
- 43. Multi-variables or Periodic attributes Time- Series prediction (WEKA) • Output/ Future prediction 43
- 44. Homework 44
- 45. Homework • Calculate the invisible states from visible series of dice [1 6 3 5 2 7 3 5 2 4] • Continue to improve performance in WEKA sales order prediction • Change algorithms • Add more observation data • If we don’t use Periodic attributes or Overlay data 45