CHAPTER 4 STOCK PRICE PREDICTION USING MODIFIED K-NEAREST NEIGHBOR (MKNN) ALGORITHM

CHAPTER 4 STOCK PRICE PREDICTION USING MODIFIED K-NEAREST NEIGHBOR (MKNN) ALGORITHM 4.1 Introduction Nowadays money investment in stock market gains major attention because of its dynamic nature. So the significant issue in market finance is discovering well organized approaches to outline and envision the stock market information to provide individuals or organizations helpful data about the behavior of the market for making decision about investment.the huge amount of important information produced by the stock market has attracted researchers to investigate this issue utilizing distinctive approaches. Since stock markets produce huge datasets it data mining techniques is found to be more efficient.data mining is utilized for excavate data from databases and discover the meaningful patterns from the database. The usefulness of this data makes data mining imperative and necessary.the essentials of data mining in finance are originating from the need to adopt specific well organized criteria to predict exactness, facilitate multi-resolution calculation. 4.2 k- Nearest Neighbor (k-nn) In pattern identification, the KNN is a technique for categorizing items according nearest training samples. KNN is a sort of illustration based learning, or lazy learning where the task is just approximated locally and all calculation is delayed until classification. 4.2.1 Assumptions in KNN KNN assumes that the information is present in a feature space. Accurately, the data points are in a metric space. Mostly these data are either multidimensional or scalar vectors. Since the points are in feature space, they have a concept of distance. This requirement is not need to be Euclidean distance yet it is used commonly. Every training sample comprises of a vectors set and separate class label corresponding with each vector. These classes may be either positive or negative classes. But KNN have the efficiency to accomplish different tasks with random number of classes.

Additionally a single number k is given. This number makes a decision of what numbers of neighbors (where neighbors are defined based on the distance metric) impact the classification. This is typically an odd number if the quantity of classes is 2. In the event that k=1, then the is just called the nearest neighbor. 4.2.2 Basics of KNN The KNN is the principal and most straightforward classification technique when the information about the distribution of the data is insufficient. This convention basically holds the whole training set during learning and allocates to every query a class characterized by the majority label of its k-nearest neighbors in the training set. The Nearest Neighbor (NN) principle is the least complex type of KNN when K = 1. In this every training samples ought to be grouped to its samples surrounded by it. Subsequently, if the classification of any of the sample data is obscure, then it could be anticipated by considering the classification of its nearest neighbor tests. Given an obscure sample and a training set consisting of samples, all the distances between the obscure sample and the entire sample in the training set can be calculated by utilizing the accompanying mathematical statement (4.1) where, x 1, x 2, x 3,x p are anticipators of the first sample and u 1, u 2,u 3, u p are anticipators of the second sample. If distance is of smallest value, then the samples in the training set is close to the obscure sample. Hence, the obscure sample may be categorized based on this nearest neighbor classification.

Known Samples Unknown Samples (a) (b) Fig 4.1 KNN decision rule Fig 4.1 illustrates the KNN decision rule for K= 1 and K= 3 for a set of samples divided into 2 classes.in Fig 4.1(a), an obscure sample (unknown sample) is categorized by using only one known sample; In Fig 4.1(b) more than one known sample is used. In the last case, the parameter K is set to 3, hence the closest three samples is considered for classifying the obscure one. Two of them belong to the same class, whereas only one belongs to the other class. In both cases, the unknown sample is classified as belonging to the class on the left. Fig 4.2 shows the pseudo code for the KNN

Input: Finite set A, Finite Set B, k, function c:b->{1,2,.n} Output: r:a->{1,2,..n} Begin For each x in A do Let L<- {} For each b in B add (a(x,b), c(b)) to L Sort the elements in L with the first components Compute the class labels from the first k elements from L Let r(x) be the class containing highest number of occurrences End Return r End Fig 4.2 Pseudo code for KNN The classifier performance is principally controlled by the decision of K and in addition the distance metric applied [20-25]. This evaluation is influenced by the sensitivity of the choosing the neighborhood size K, since local region radius is calculated by the K th nearest neighbor distance to the query and diverse value of K yields various conditional class probabilities. 4.2.2.1 Distance Metric KNN makes estimation according to the result of the K neighbors closest to that point. Accordingly, to make estimation with KNN, we have to characterize a metric for measuring the separation between the query point and cases from the samples. A familiar opinion to estimate this distance is known as Euclidean. Different measures include Euclidean square, City-square, and Chebychev. Table 4.1 presents the distance metrics and their formula.

Table 4.1 Distance metrics employed in KNN Distance Metric Formula (x- query point, p data point from unknown sample) Euclidean Distance Euclidean Squared City-block Chebychev 4.2.2.2 K-Nearest Neighbor Predictions After choosing the value of K, anticipations are made based on the KNN samples. For regression, KNN prediction is the result of average of the K nearest neighbors: (4.2) Where x i is the i th case of the sample and y is the query point anticipation (result).in classification problem, based on the voting scheme KNN anticipation is performed in which the winner is used to name the query. Generally the K neighbors have equivalent impact on prediction regardless of their relative distance from the query point. An optional methodology is to use randomly large K values with more vitality given to cases nearest to the query point. This is accomplished by using 'distance weighting'. 4.2.2.3Distance Weighting Since KNN forecasts are based on the belief that items close in distance are conceivably similar, it is good to differentiate between the K nearest neighbors during prediction, i.e., let the closest points among the K nearest neighbors have more say in influencing the result of the query point. This can be attained by presenting a set of weights W, one for every nearest neighbor, characterized by the relative closeness of each one neighbor regarding the query point. Thus

(4.3) Where is the distance between the query point x and the i th case p i of the sample. It is clear that the weights defined in this manner above will satisfy: (4.4) Thus, for regression problems, we have: (4.5) For classification problems, the highest value of the above equation is taken for every one of class variables. It is obvious from the above equation that when K>1, one can basically characterize the standard deviation for predictions in regression tasks using, (4.6) Some of the KNN merits are depicted as follows: Easy to use; resilient to noisy training samples, particularly if the inverse square of weighted distance is used as the "distance" measure; and Effective if the training data is vast. In spite of these advantages, it has a few demerits such as: a) computationally expensive as it needs to find distance of each one query example to all training sample data; b) The huge memory to execute in extent with size of training set; c) Low precision rate in multidimensional datasets; d) Need to find the parameter value K, the quantity of nearest neighbors; e) Distance based learning is not clear which sort of distance to use; and f) decide which labels are ideal to produce the best results. Therefore, to overcome the low precision rate of KNN, Modified KNN (MKNN) has been proposed in this research work. The MKNN preprocesses the training set before using it and finds the legitimacy of any training data.the final classification is then made by applying weighted KNN which used validity as the multiplicative factor. 4.3 Modified K-Nearest Neighbor (MKNN) In this research Modified K-Nearest Neighbor Algorithm is used for prediction of stock index movement.the fundamental idea of the presented technique is allocating the class label of the

queried instance into K validated data training points and the validity of all data tests in the training set is calculated. At that point, a weighted KNN is performed on any trained samples. Fig 4.3 demonstrates the pseudo code of the MKNN. Pseudo-code of the MKNN Algorithm End Output_label:= MKNN ( train_set, test_sample) Begin For i := 1 to train_size Validity(i) := Compute Validity of i-th sample; End for; Output_label:=Weighted_KNN(Validity,test_sample); Return Output_label; Fig 4.3 Pseudo code of the MKNN 4.3.1 Data and Sources of Data This exploration inspects the monthly change of closing values of NSE-NIFTY and BSE stock data according to the following predictors: Open price, High price, Low price and Close price. NSE-NIFTY and BSE stock index values are acquired from the NSE and BSE sites separately for the period from Jan'2013 to Dec 2013. The data is split into two sub-tests of 80:20 where the in-test sample or preparing data compasses from Jan' 2010 to Dec' 2012 and the data for the remaining period from Jan 2013 to Dec 2013are used for out-of sample or test data. 4.3.2 Preprocessing the data When the data was gathered at first, all the values of the attributes chosen were continuous numeric values. Data conversion was applied by generalizing the data to a higher-level concept so as all the values got to be discrete. The rule that was made to convert the numeric values of each one attribute to discrete values relied on upon the earlier day closing price of the stock. If in case that the values of the properties open, high, low, and close were more prominent than the estimation of attribute past for the same trading day, the numeric values of the attribute were supplanted by the value positive. In the event that the values of the attributes said above were

short of what the value of the attributes used previously, the numeric values of the attributes were supplanted by negative. If the values of those attributes were equal to the value of the attribute previous,then values were replaced by the same equal value. 4.3.3 Building the Model After the data has been arranged and converted, the upcoming step was to build the forecast model using the MKNN. The MKNN was chosen since the development of MKNN classifiers does not require any domain information, along these lines it is fitting for exploratory learning discovery. Also, it can deal with high dimensional data. In the MKNN, each sample in training set must be validated at the first step. The validity of each one point is found as per its neighbors. The validation procedure is performed for all train samples. To accept a sample point in the training set, the H nearest neighbors of the point is considered. Among the H nearest neighbors of a training test x, validity(x) enumerate the quantity of points with the same name to the label of x. The formula which is proposed to calculate the validity of every point in train set is (4.7) where H is the number of considered neighbors and lbl(x)returns the true class label of the sample x. also, Ni(x) stands for the i th nearest neighbor of the point x. The function S takes into account the similarity between the point x and the i th nearest neighbor. (4.8) 4.3.3.1 Prediction Model The prediction model considers Opening value, High value, Low value and Closing value of the market index as independent variables and the next day s closing value as the dependent variable. The MKNN identifies k nearest neighbors in the training data set in terms of the Euclidean distance with respect to the day for which prediction is to be done. Once k- nearest neighbors are identified, the prediction for that day is computed as the average of the next day s closing prices of those neighbors. The MKNN employs weighted KNN on the test

data set for predicting the next day s closing value. The output of the predictive model is compared with the actual values of the test dataset for validation. Applying weighted KNN Each of the K samples is given a weighted vote that is usually equal to some decreasing function of its distance from the unknown sample. For example, the vote might set be equal to 1/(de+1), where de is Euclidian distance. These weighted votes are then summed for each class, and the class with the largest total vote is chosen. This distance weighted KNN technique is very similar to the window technique for estimating density functions. For example, using a weighted of 1/ (de+1) is equivalent to the window technique with a window function of 1/ (de+1) if K is chosen equal to the total number of training samples. In the MKNN method, first the weight of each neighbor is computed using (4.9) Then, the validity of that training sample is multiplied on its raw weight which is based on the Euclidian distance. In the MKNN method, the weight of each neighbor sample is derived according to (4.10) Here v (i) and Val (i) stand for the weight and the validity of the i th nearest sample in the train set. 4.3.3.2 Classifier Model The classifier model considers opening value, high value, low value, closing value and returns of the market index as independent variables and the next day s class as the dependent variable. Returns for a day is calculated as (4.11)

Where v t is the closing value of the index on the current day and v t-1 is the closing value of the index of previous day. If the next days return is positive, the next day s class is classified as bull otherwise bear.the yield of the classifier is compared with the real classes of the test data set to improve the effectiveness of the approach. 4.4 Empirical Results The examined data sample comprises of daily returns from January 2010 to December 2013 of three stock market indices, BSE oil and gas, CNX-100 and CNX-NIFTY. Data samples are collected from the historical values of NSE- NIFTY and BSE (Bombay Stock Exchange) data. The total data set is split into two one for training the network and remaining for testing the performance of the network. In this experiment, the stock index data from January 2010 to December 2012 is used to train the network and the data from January 2013 to December 2013 is used to test the performance of the proposed approach. 4.4.1 Performance Measures The following performance measures are used to gauge the performance of the trained forecasting model for the test data: The Mean Squared Error (MSE), Root Mean Squared Error (RMSE), R-Squared (R 2 ), Adjusted R-squared (RA 2 ), Hannan-Quinn Information Criterion (HQ). Table 4.2 illustrates various performance measures that are used to evaluate the effectiveness of the proposed approach.

Table 4.2: Performance Criteria and the related formula Performance Criteria Mean Squared Error Formula Root Mean Squared Error (RMSE) R-Squared(R 2 ) Adjusted R-Squared(R A 2 ) = real value, = estimated value, = mean value Hannan-Quinn Information Criterion (HQ) SSR = 4.4.2 Results 4.4.2.1 Prediction Model Fig 4.4 presents the results for the returns (close price) for the year 2013 of the BSE Oil and Gas index obtained using Modified KNN (MKNN) and table 4.3 shows the error rate of the proposed approach using various performance measures.

Jan Feb Mar April May June July Aug Sep Oct Nov Dec Close Price 100 95 90 85 80 75 70 65 60 55 50 Actual Predicted Fig 4.4 BSE Predicted Close Price Value Table 4.3 Error Rate of BSE Test Criteria Error Rate (%) Mean Squared Error 3.87 Root Mean Squared Error (RMSE) 5.98 R-Squared(R 2 ) 0.35 Adjusted R-Squared(R 2 A ) 1.67 Hannan-Quinn Information Criterion (HQ) -5.03

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Close Price Fig 4.5 presents the results for the returns (close price) for the year 2013 of the NSE CNX 100 index and table 4.4 shows the error rate of the MKNN approach using various performance measures. 64 62 60 58 56 54 52 50 Actual Predicted Fig 4.5 Predicted Close Price of CNX-100 Stock Index Table 4.4 Error Rate of CNX-100 Stock Index Test Criteria Error Rate (%) Mean Squared Error 3.67 Root Mean Squared Error (RMSE) 4.98 R-Squared(R 2 ) 0.38 Adjusted R-Squared(R 2 A ) 1.98 Hannan-Quinn Information Criterion (HQ) -5.03

Jan Feb Mar April May Jun Jul Aug Sep Oct Nov Dec Close Price Fig 4.6 presents the results for the returns (close price) for the year 2013 of the NSE CNX NIFTY index and table 4.5 shows the error rate of the proposed approach using various performance measures. 64 62 60 58 56 54 52 50 Actual Predicted Fig 4.6 Predicted Close Price of CNX-NIFTY Stock Index Table 4.5 Error Rate of CNX-NIFTY Stock Index Test Criteria Error Rate (%) Mean Squared Error 3.89 Root Mean Squared Error (RMSE) 4.43 R-Squared(R 2 ) 0.45 Adjusted R-Squared(R 2 A ) 1.78 Hannan-Quinn Information Criterion (HQ) -5.03

4.2.2.2 Classification Model The results obtained from the two classifying models for BSE oil and gas, CNX-100 and CNX- NIFTY are given below. Table 4.6 Comparison of Classifier Models on the Test Dataset for BSE Oil and Gas k-nn MKNN Instances Accuracy Instances Accuracy Correctly classified Incorrectly classified 258 77.9% 294 88.8% 73 22.1% 37 12.2% Table 4.6 shows that the MKNN rightly classifies the next day s index movement of BSE Oil and Gas Index for 294 instances out of the total of 331 instances with an accuracy rate of 88.8% and misclassifies 37instances with an error rate of 12.2%.But the KNN correctly classifies the next day s index movement only for 258 instances out of the total of 331 instances with an accuracy rate of 77.9% and misclassifies 73 instances with an error rate of 22.1% respectively. Table 4.7 Comparison of Classifier Models on the Test Dataset for CNX-100 k-nn MKNN Instances Accuracy Instances Accuracy Correctly classified Incorrectly classified 254 76.89% 290 88.01% 77 22.87% 41 12.79% Table 4.7 shows that the MKNN rightly classifies the next day s index movement of CNX-100 Index for 294 instances out of the total of 331 instances with an accuracy rate of 88.01% and misclassifies 41 instances with an error rate of 12.79% respectively.but the KNN correctly classifies the next day s index movement only for 254 instances out of the total of 331

instances with an accuracy rate of 76.89% and misclassifies 77 instances with an error rate of 22.87% respectively. Table 4.8Comparison of Classifier Models on the Test Dataset for CNX-NIFTY Correctly classified Incorrectly classified k-nn MKNN Instances Accuracy Instances Accuracy 256 77.01% 295 88.57% 75 22.45% 36 11.98% Table 4.8 shows that the MKNN rightly classifies the next day s index movement of CNX-NIFTY Index for 295 instances out of the total of 331 instances with an accuracy rate of 88.57% and misclassifies 36instances with an error rate of 11.98% respectively. But the KNN correctly classifies the next day s index movement only for 256 instances out of the total of 331 instances with an accuracy rate of 77.01% and misclassifies 75 instances with an error rate of 22.45% respectively. Table 4.9Confusion Matrices for BSE Oil and Gas K-NN MKNN Algorithm Actual Class Predicted Class Predicted Class Bull Bear Bull Bear Bull 104 60 150 14 Bear 19 148 9 158 It is seen from the Table 4.9 that MKNN rightly classifies 150 bull class instances out of the total of 164 bull class instances and rightly classifies158 bear class instances out of the total of 167 bear class instances. But the KNN has lower performance compared to the MKNN model.

Table 4.10Confusion Matrices for CNX-100 K-NN MKNN Algorithm Actual Class Predicted Class Predicted Class Bull Bear Bull Bear Bull 100 64 149 15 Bear 22 145 12 155 Table 4.10 shows that MKNN rightly classifies 149 bull class instances out of the total of 164 bull class instances while KNN classifies only about 100 instances and MKNN correctly classifies158 bear class instances out of the total of 167 bear class instances which is about 145 instances in bear class. Table 4.11 Confusion Matrices for CNX-NIFTY K-NN MKNN Algorithm Actual Class Predicted Class Predicted Class Bull Bear Bull Bear Bull 101 63 151 13 Bear 21 146 11 156 Table 4.11 shows that MKNN rightly classifies 151 bull class instances out of the total of 164 bull class instances while KNN classifies only about 101 instances and MKNN correctly classifies156 bear class instances out of the total of 167 bear class instances which is about 146 instances in bear class.