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Katsanos",authors:[{id:"169242",title:"Dr.",name:"Sunday",middleName:"Onyebuchi",surname:"Nwaubani",fullName:"Sunday Nwaubani",slug:"sunday-nwaubani"}]},{id:"46235",title:"Corrosion Detection for Automated Visual Inspection",slug:"corrosion-detection-for-automated-visual-inspection",signatures:"Francisco Bonnin-Pascual and Alberto Ortiz",authors:[{id:"124589",title:"Prof.",name:"Alberto",middleName:null,surname:"Ortiz",fullName:"Alberto Ortiz",slug:"alberto-ortiz"},{id:"169256",title:"Ph.D. Student",name:"Francisco",middleName:null,surname:"Bonnin-Pascual",fullName:"Francisco Bonnin-Pascual",slug:"francisco-bonnin-pascual"}]},{id:"46219",title:"Corrosion of Biomaterials Used in Dental Reconstruction Dentistry",slug:"corrosion-of-biomaterials-used-in-dental-reconstruction-dentistry",signatures:"I. Patrascu, E. Vasilescu, E. Gatin and R.R. Cara-Ilici",authors:[{id:"169224",title:"Dr.",name:"Ion",middleName:null,surname:"Patrascu",fullName:"Ion Patrascu",slug:"ion-patrascu"},{id:"170546",title:"Dr.",name:"V.",middleName:null,surname:"Vasilescu",fullName:"V. Vasilescu",slug:"v.-vasilescu"},{id:"152661",title:"Dr",name:"R.",middleName:null,surname:"Cara-Ilici",fullName:"R. Cara-Ilici",slug:"r.-cara-ilici"},{id:"153007",title:"Prof.",name:"Eduard",middleName:null,surname:"Gatin",fullName:"Eduard Gatin",slug:"eduard-gatin"}]},{id:"46216",title:"Investigation of Al-Fe Aerospace Alloy Laser-Treated with Different Corrosion Characterization Techniques",slug:"investigation-of-al-fe-aerospace-alloy-laser-treated-with-different-corrosion-characterization-techn",signatures:"Moisés Meza Pariona",authors:[{id:"38666",title:"Ph.D.",name:"Moises",middleName:"Meza",surname:"Pariona",fullName:"Moises Pariona",slug:"moises-pariona"}]},{id:"46244",title:"Developments in Reliability-Based Assessment of Corrosion",slug:"developments-in-reliability-based-assessment-of-corrosion",signatures:"Zahiraniza Mustaffa",authors:[{id:"169262",title:"Dr.",name:"Zahiraniza",middleName:null,surname:"Mustaffa",fullName:"Zahiraniza Mustaffa",slug:"zahiraniza-mustaffa"}]}]}]},onlineFirst:{chapter:{type:"chapter",id:"74027",title:"Stock Market Trend Prediction Using Hidden Markov Model",doi:"10.5772/intechopen.93988",slug:"stock-market-trend-prediction-using-hidden-markov-model",body:'The fundamental idea behind a hidden Markov model is that there is a Markov process we cannot observe that determines the probability distribution for what we do observe. Thus a hidden Markov model is specified by the transition density of the Markov chain and the probability laws that govern what we observe given the state of the Markov chain. Given such a model, we want to estimate any parameters that occur in the model. And also determined the most likely sequence for the hidden process. Finally we may want the probability distribution for the hidden states at every location.
Let
Our model is then described by the sets of probability distributions
The measure of best is to find the path that has the maximum probability in the HMM, given the sequence
Hidden Markov model (HMM) is a stochastic model which is not directly observable, It describes the observable events that are depends on internal factors. The observable events are represented as symbols, where the invisible factor involved in the observation is represented as a state. HMM is a stochastic model where the system is assumed to be a Markov Process with hidden states and it gives better accuracy than the other models. Using the given input values, the parameters of the HMM (λ) denoted by A, B and π are found out. An HMM is defined as λ = (S,O,A,B,π) where S = {s1,s2,…,sN} is a set of N possible states O = {o1,o2,…,oM} is a set of M possible observation symbols, A is an N*N state Transition Probability Matrix (TPM), B is an N*M observation or Emission Probability Matrix (EPM) and Π is an N dimensional initial state probability distribution vector and A,B and π should satisfy the following conditions (Figure 1):
Diagram of HMM.
Given the HMM = {A,B,π} and the observation sequence O = o1,o2,…,oM, the probability that model λ has generated sequence O is calculated. Often this problem is solved by the Forward Backward Algorithm [7, 8].
Given the HMM λ = {A,B,π} and the observation sequence O = o1,o2,…,oM, calculate the most likely sequence of hidden states that produced this observation sequence O. Usually this problem is handled by Viterbi Algorithm [7, 8].
Given some training observation sequences O = o1,o2,…,oM, and general structure of HMM (numbers of hidden and visible states), determine HMM parameters λ = {A,B,π} that best fit training data. The most common solution for this problem is Baum-Welch algorithm [9, 10] which is considered as the traditional method for training HMM.
In this chapter, the data has been taken from
Here two observing symbols “I” for Increasing states and the symbols “D” for decreasing states have been used. If the differences of close value greater than 0 its observing that the symbol is “f” and If the differences of close value less than 0 its observing that the symbol is “D”. There are six hidden states assumed and are denoted by the symbol S1, S2, S3, S4, S5, S6 are indicates that very low, low, moderate low, moderate high, high and very high respectively. The states are not directly observable.
The situations of the stock market are considered hidden. Given a sequence of observation we can find the hidden state sequence that produced those observations. Table 1 shows the daily close value of the stock market.
S. no | Date | Close |
---|---|---|
1 | 01/02/2020 | 41,626.64 |
2 | 01/03/2020 | 41,464.61 |
3 | 01/06/2020 | 40,676.63 |
4 | 01/07/2020 | 40,869.47 |
5 | 01/08/2020 | 40,817.74 |
6 | 01/09/2020 | 41,452.35 |
7 | 01/10/2020 | 41,599.72 |
8 | 01/13/2020 | 41,859.69 |
9 | 01/14/2020 | 41,952.63 |
10 | 01/15/2020 | 41,872.73 |
11 | 01/16/2020 | 41,932.56 |
12 | 01/17/2020 | 41,945.37 |
13 | 01/20/2020 | 41,528.91 |
14 | 01/21/2020 | 41,323.81 |
15 | 01/22/2020 | 41,115.38 |
16 | 01/23/2020 | 41,386.4 |
17 | 01/24/2020 | 41,613.19 |
18 | 01/27/2020 | 41,155.12 |
19 | 01/28/2020 | 40,966.86 |
20 | 01/29/2020 | 41,198.66 |
21 | 01/30/2020 | 40,913.82 |
22 | 01/31/2020 | 40,723.49 |
Daily close value of NSE.
Interval values:
S1 = −9500 to −551.
S2 = −550 to −251.
S3 = −250 to 249.
S4 = 250 to 8500.
S. no | c.v | D in 1 day CV | o.s | D in 2 days CV | o.s | D in3 days CV | o.s | D in 4 day CV | o.s | D in 5 day CV | o.s | D in6 days CV | o.s |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 41,626.64 | ||||||||||||
2 | 41,464.61 | 162.03 | I | ||||||||||
3 | 40,676.63 | 787.98 | I | −625.95 | D | ||||||||
40,869.47 | −192.84 | D | 980.82 | I | −1606.77 | D | |||||||
5 | 40,817.74 | 51.73 | I | −244.57 | D | 1225.39 | I | −2882.16 | D | ||||
6 | 41,452.35 | −634.61 | D | 686.84 | I | −930.91 | D | 2156.3 | I | −4988.46 | D | ||
7 | 41,599.72 | −147.37 | D | −487.24 | D | 1173.58 | I | 2104.49 | I | 4260.79 | I | −9249.25 | D |
8 | 41,759.69 | −259.97 | D | 112.6 | I | −599.84 | D | 1773.42 | I | −3877.91 | D | 8138.7 | I |
9 | 41,952.63 | −92.94 | D | −167.03 | D | 279.63 | I | −879.47 | D | 2652.89 | I | −6530.8 | D |
10 | 41,872.73 | 79.9 | I | −172.84 | D | 5.81 | I | 273.82 | I | −1153.28 | D | 3806.18 | I |
11 | 41,932.56 | −59.83 | D | 139.73 | I | −312.57 | D | 318.38 | I | −44.56 | D | −1108.73 | D |
12 | 41,945.37 | −12.81 | D | −47.02 | D | −92.71 | D | 405.28 | I | −86.9 | D | 42.34 | I |
13 | 41,528.91 | 416.46 | I | 403.65 | I | −450.67 | D | 357.96 | I | 47.32 | I | −134.22 | D |
14 | 41,323.81 | 205.1 | I | 211.36 | I | 192.22 | I | −642.96 | D | 1000.92 | I | −953.6 | D |
15 | 41,115.38 | 208.43 | I | −3.33 | D | 214.69 | I | −22.4 | D | −620.56 | D | 1621.48 | I |
16 | 41,386.4 | −271.02 | D | 479.45 | I | −482.78 | D | 697.47 | I | −719.87 | D | 99.31 | I |
17 | 41,613.19 | −226.79 | D | −44.23 | D | 523.68 | I | −1006.46 | D | 1703.93 | I | −2423.8 | D |
18 | 41,155.12 | 458.01 | I | −684.86 | D | 640.63 | I | −116.95 | D | −889.51 | D | 2593.44 | I |
19 | 40,966.86 | 188.26 | I | 269.81 | I | −415.05 | D | 1055.68 | I | 938.73 | I | −1828.24 | D |
20 | 41,198.66 | −231.8 | D | 420.06 | I | −150.25 | D | −264.8 | D | 1320.48 | I | −381.75 | D |
21 | 40,913.82 | 284.84 | I | −516.64 | I | 936.7 | I | −1086.95 | D | 822.15 | I | 498.33 | I |
22 | 40,723.49 | 190.33 | I | 94.51 | I | −611.15 | D | 1547.85 | I | −2634.8 | D | 3456.95 | I |
Daily close value for finding differences in one day, two day, three days, four days, five days, six days close value.
The various probability values of TPM, EPM and π for difference in one day, two days, three days, four days, five days, six days close value are calculated as given below (Table 2).
S1 | S2 | S3 | S4 | |||||
---|---|---|---|---|---|---|---|---|
I | D | I | D | I | D | I | D | |
S1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
S2 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
S3 | 0.071 | 0 | 0.071 | 0 | 0.1429 | 0.2857 | 0 | 0.4286 |
S4 | 0 | 0 | 0 | 0.8 | 0.2 | 0 | 0 | 0 |
Transitions with probability values for one day close value.
Probability values of TPM, EPM, and π for difference in one day close value (Figure 2 and Table 3):
Diagram of TPM day 1.
S1 | S2 | S3 | S4 | |||||
---|---|---|---|---|---|---|---|---|
I | D | I | D | I | D | I | D | |
S1 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0.5 |
S2 | 0 | 0 | 0 | 0 | 0.5 | 0.5 | 0 | 0 |
S3 | 0 | 0.111 | 0 | 0 | 0.3333 | 0.2222 | 0.1111 | 0.2222 |
S4 | 0 | 0 | 0.3333 | 0 | 0.5 | 0 | 0.1667 | 0 |
Transition table with probability values for difference in two day close value.
Probability values of TPM, EPM, and π for difference in two day close value (Figure 3 and Table 4).
Diagram of TPM day 2.
S1 | S2 | S3 | S4 | |||||
---|---|---|---|---|---|---|---|---|
I | D | I | D | I | D | I | D | |
S1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
S2 | 0 | 0 | 0 | 0 | 0 | 0.75 | 0 | 0.25 |
S3 | 0 | 0 | 0.4 | 0.2 | 0.2 | 0 | 0 | 0.2 |
S4 | 0.5 | 0 | 0.2 | 0 | 0.2 | 0 | 0.2 | 0 |
Transition table with probability values for difference in three day close value.
Probability values of TPM, EPM, and π for difference in three day close value (Figure 4 and Table 5):
Diagram of TPM day 3.
S1 | S2 | S3 | S4 | |||||
---|---|---|---|---|---|---|---|---|
I | D | I | D | I | D | I | D | |
S1 | 0.1429 | 0.2429 | 0 | 0.1429 | 0 | 0.1429 | 0 | 0.4286 |
S2 | 0.5 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 |
S3 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
S4 | 0.4286 | 0 | 0.1429 | 0 | 0 | 0 | 0.4286 | 0 |
Transition table with probability values for difference in four day close value.
Probability values of TPM, EPM and π for difference in four days close value (Figure 5 and Table 6):
Diagram of TPM day 4.
S1 | S2 | S3 | S4 | |||||
---|---|---|---|---|---|---|---|---|
I | D | I | D | I | D | I | D | |
S1 | 0 | 0.1667 | 0 | 0 | 0 | 0.1667 | 0 | 0.6667 |
S2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S3 | 0 | 0 | 0 | 0 | 0 | 0.6667 | 0.3333 | 0 |
S4 | 0.7143 | 0 | 0 | 0 | 0 | 0 | 0.2857 | 0 |
Transition table with probability values for difference in five day close value.
Probability values of TPM, EPM and π for difference in five days close value (Figure 6 and Table 7):
Diagram of TPM day 5.
S1 | S2 | S3 | S4 | |||||
---|---|---|---|---|---|---|---|---|
I | D | I | D | I | D | I | D | |
S1 | 0 | 0 | 0 | 0.2 | 0 | 0.2 | 0 | 0.6 |
S2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
S3 | 0.3333 | 0.3333 | 0 | 0 | 0.3333 | 0 | 0 | 0 |
S4 | 0.5 | 0 | 0 | 0 | 0.25 | 0 | 0.25 | 0 |
Transition table with probability values for difference in six day close value.
Probability values of TPM, EPM and π for difference in six days close value (Figure 7 and Table 8):
Diagram of TPM day 6.
The various transitions probability values for difference in one day to six days close values are displayed in Figure 2 to Figure 7 respectively.
Optimum Sequence of States:
To generate a random sequence of emission symbols and states are calculated by using the function “Hmmgenerate”. The HMM matlab toolbox syntax is: [Sequence,States] = Hmmgenerate(L,TPM,EPM). The length of both sequence and state to be generated is denoted by L [11]. The fitness function used for finding the fitted value of sequence of states is defined by
Using the iterative procedure, for each TPM and EPM framed we get an optimum sequence of states generated.
The length of the sequence taken as L = 4 and the optimum sequence of states obtained from the all six day’s differences with TPM and EPM is given in the below and here ‘ε’ is the start symbol.
1. | ε | → | I S4 | → | D S4 | → | I S3 | → | D S4 |
2. | ε | → | D S1 | → | I S4 | → | I S4 | → | D S3 |
3. | ε | → | I S4 | → | I s2 | → | D S3 | → | D S1 |
4. | ε | → | D S1 | → | D S4 | → | I S3 | → | D S4 |
5. | ε | → | I S3 | → | I S3 | → | D S2 | → | D S4 |
6. | ε | → | I S4 | → | D S1 | → | I S3 | → | D S4 |
Here, the one day difference of TPM and EPM has the shortest path. So the best optimum sequence is found from one day difference in close value. Using the fitness function we compute the fitness value for each of the optimum sequences of states obtained (Table 9).
S. no. | Comparison of six optimum sequence of states | Calculated value | Fitness = |
---|---|---|---|
1 | (1,2) + (1,3) + (1,4) | 1 | 1 |
2 | (2,1) + (2,3) + (2,4) | 1.7 | 0.588 |
3 | (3,1) + (3,2) + (3,4) | 2.425 | 0.412 |
4 | (4,1) + (4,2) + (4,3) | 3.15 | 0.32 |
Comparison of six optimum state sequences.
In column four the highest value is the fitness value and the better is the performance of the particular sequence.
Stock prediction is challenging due to its randomness. Hidden Markov Model can be used for stock prediction by finding hidden patterns. Here the Hidden Markov model easily recognized four states of the stock market and also it was used to predict the future values. The highest value in the Optimum State Sequences is the better performance of the particular sequence. Hidden states and sequences have been generated to easily identify the level of the sequence whether the next day value is increasing. And also identified whether the increasing level is moderate high or high or very high and also decreasing level whether moderate low or low or very low. This model will be very much useful for short term as well as long term investors.
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\\n"}]'},components:[{type:"htmlEditorComponent",content:'Copyright is the term used to describe the rights related to the publication and distribution of original Works. Most importantly from a publisher's perspective, copyright governs how Authors, publishers and the general public can use, publish, and distribute publications.
\n\nIntechOpen only publishes manuscripts for which it has publishing rights. This is governed by a publication agreement between the Author and IntechOpen. This agreement is accepted by the Author when the manuscript is submitted and deals with both the rights of the publisher and Author, as well as any obligations concerning a particular manuscript. However, in accepting this agreement, Authors continue to retain significant rights to use and share their publications.
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\n\n\n\n
LICENSE | \n\t\t\tUSED FROM - | \n\t\t\tUP TO - | \n\t\t
\n\t\t\t Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0) \n\t\t\t | \n\t\t\t\n\t\t\t 1 July 2005 (2005-07-01) \n\t\t\t | \n\t\t\t\n\t\t\t 3 October 2011 (2011-10-03) \n\t\t\t | \n\t\t
Creative Commons Attribution 3.0 Unported (CC BY 3.0) | \n\t\t\t\n\t\t\t 5 October 2011 (2011-10-05) \n\t\t\t | \n\t\t\tCurrently | \n\t\t
The CC BY 3.0 license permits Works to be freely shared in any medium or format, as well as the reuse and adaptation of the original contents of Works (e.g. figures and tables created by the Authors), as long as the source Work is cited and its Authors are acknowledged in the following manner:
\n\nContent reuse:
\n\n© {year} {authors' full names}. Originally published in {short citation} under {license version} license. Available from: {DOI}
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\n\n© {year} {authors' full names}. Adapted from {short citation}; originally published under {license version} license. Available from: {DOI}
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\n\nContent reuse:
\n\n© {year} {authors' full names}. Originally published in {short citation} under {license version} license. Available from: {DOI}
\n\nContent adaptation & reuse:
\n\n© {year} {authors' full names}. Adapted from {short citation}; originally published under {license version} license. Available from: {DOI}
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\n\nOriginally published in {full citation}. Available from: {DOI}
\n\nAll Book cover design elements, as well as Video image graphics are subject to copyright by IntechOpen.
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\n\nAll Video Lectures under IntechOpen's production are subject to copyright and are property of IntechOpen, unless defined otherwise, and are licensed under the Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) license. This grants all others the right to:
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\n\nUsers wishing to repost and share the Video Lectures are welcome to do so as long as they acknowledge the source in the following manner:
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\n\nUsers wishing to reuse, modify, or adapt the Video Lectures in a way not permitted by the license are welcome to contact us at permissions@intechopen.com to discuss waiving particular license terms.
\n\nAll software used on the IntechOpen platform, any used during the publishing process, and the copyright in the code constituting such software, is the property of IntechOpen or its software suppliers. As such, it may not be downloaded or copied without permission.
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\n\nAll content included on IntechOpen Websites not forming part of contributed materials (such as text, images, logos, graphics, design elements, videos, sounds, pictures, trademarks, etc.), are subject to copyright and are property of, or licensed to, IntechOpen. Any other use, including the reproduction, modification, distribution, transmission, republication, display, or performance of the content on this site is strictly prohibited.
\n\nPolicy last updated: 2016-06-08
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