Time Series Data Cleaning: A Survey <s> B. MARKOV MODEL <s> In this article I present a new approach to model more realistically the variability of financial time series. I develop a Markov-ARCH model that incorporates the features of both Hamilton's switching-regime model and Engle's autoregressive conditional heteroscedasticity (ARCH) model to examine the issue of volatility persistence in the monthly excess returns of the three-month treasury bill. The issue can be resolved by taking into account occasional shifts in the asymptotic variance of the Markov-ARCH process that cause the spurious persistence of the volatility process. I identify two periods during which there is a regime shift, the 1974:2–1974:8 period associated with the oil shock and the 1979:9–1982:8 period associated with the Federal Reserve's policy change. The variance approached asymptotically in these two episodes is more than 10 times as high as the asymptotic variance for the remainder of the sample. I conclude that regime shifts have a greater impact on the properties of the data, and I ca... <s> BIB001 </s> Time Series Data Cleaning: A Survey <s> B. MARKOV MODEL <s> We form a finite-state Markov channel model to represent Rayleigh fading channels. We develop and analyze a methodology to partition the received signal-to-noise ratio (SNR) into a finite number of states according to the time duration of each state. Each state corresponds to a different channel quality indicated by the bit-error rate (BER). The number of states and SNR partitions are determined by the fading speed of the channel. Computer simulations are performed to verify the accuracy of the model. <s> BIB002 </s> Time Series Data Cleaning: A Survey <s> B. MARKOV MODEL <s> In this paper we propose and implement a fusion model by combining the Hidden Markov Model (HMM), Artificial Neural Networks (ANN) and Genetic Algorithms (GA) to forecast financial market behaviour. The developed tool can be used for in depth analysis of the stock market. Using ANN, the daily stock prices are transformed to independent sets of values that become input to HMM. We draw on GA to optimize the initial parameters of HMM. The trained HMM is used to identify and locate similar patterns in the historical data. The price differences between the matched days and the respective next day are calculated. Finally, a weighted average of the price differences of similar patterns is obtained to prepare a forecast for the required next day. Forecasts are obtained for a number of securities in the IT sector and are compared with a conventional forecast method. <s> BIB003 </s> Time Series Data Cleaning: A Survey <s> B. MARKOV MODEL <s> In this paper, a novel framework and methodology based on hidden semi-Markov models (HSMMs) for high PM"2"."5 concentration value prediction is presented. Due to lack of explicit time structure and its short-term memory of past history, a standard hidden Markov model (HMM) has limited power in modeling the temporal structures of the prediction problems. To overcome the limitations of HMMs in prediction, we develop the HSMMs by adding the temporal structures into the HMMs and use them to predict the concentration levels of PM"2"."5. As a model-driven statistical learning method, HSMM assumes that both data and a mathematical model are available. In contrast to other data-driven statistical prediction models such as neural networks, a mathematical functional mapping between the parameters and the selected input variables can be established in HSMMs. In the proposed framework, states of HSMMs are used to represent the PM"2"."5 concentration levels. The model parameters are estimated through modified forward-backward training algorithm. The re-estimation formulae for model parameters are derived. The trained HSMMs can be used to predict high PM"2"."5 concentration levels. The validation of the proposed framework and methodology is carried out in real world applications: prediction of high PM"2"."5 concentrations at O'Hare airport in Chicago. The results show that the HSMMs provide accurate predictions of high PM"2"."5 concentration levels for the next 24h. <s> BIB004 </s> Time Series Data Cleaning: A Survey <s> B. MARKOV MODEL <s> Stock market prediction is a classic problem which has been analyzed extensively using tools and techniques of Machine Learning. Interesting properties which make this modeling non-trivial is the time dependence, volatility and other similar complex dependencies of this problem. To incorporate these, Hidden Markov Models (HMM's) have recently been applied to forecast and predict the stock market. We present the Maximum a Posteriori HMM approach for forecasting stock values for the next day given historical data. In our approach, we consider the fractional change in Stock value and the intra-day high and low values of the stock to train the continuous HMM. This HMM is then used to make a Maximum a Posteriori decision over all the possible stock values for the next day. We test our approach on several stocks, and compare the performance to some of the existing methods using HMMs and Artificial Neural Networks using Mean Absolute Percentage Error (MAPE). <s> BIB005 </s> Time Series Data Cleaning: A Survey <s> B. MARKOV MODEL <s> RFID is widely used for object tracking in indoor environments, e.g., airport baggage tracking. Analyzing RFID data offers insight into the underlying tracking systems as well as the associated business processes. However, the inherent uncertainty in RFID data, including noise (cross readings) and incompleteness (missing readings), pose challenges to high-level RFID data querying and analysis. In this paper, we address these challenges by proposing a learning-based data cleansing approach that, unlike existing approaches, requires no detailed prior knowledge about the spatio-temporal properties of the indoor space and the RFID reader deployment. Requiring only minimal information about RFID deployment, the approach learns relevant knowledge from raw RFID data and uses it to cleanse the data. In particular, we model raw RFID readings as time series that are sparse because the indoor space is only partly covered by a limited number of RFID readers. We propose the Indoor RFID Multi-variate Hidden Markov Model (IR-MHMM) to capture the uncertainties of indoor RFID data as well as the correlation of moving object locations and object RFID readings. We propose three state space design methods for IR-MHMM that enable the learning of parameters while contending with raw RFID data time series. We solely use raw uncleansed RFID data for the learning of model parameters, requiring no special labeled data or ground truth. The resulting IR-MHMM based RFID data cleansing approach is able to recover missing readings and reduce cross readings with high effectiveness and efficiency, as demonstrated by extensive experimental studies with both synthetic and real data. Given enough indoor RFID data for learning, the proposed approach achieves a data cleansing accuracy comparable to or even better than state-of-the-art techniques requiring very detailed prior knowledge, making our solution superior in terms of both effectiveness and employability. <s> BIB006
Markov process is a class of stochastic processes, which means that the transition of each state in the process depends only on the previous n states. This process is called a n−order model, where n is the number that affects the transition state. The simplest Markov process is the first − order process, and the transition of each state depends only on the state before it. Time and state are discrete Markov processes called Markov chains, abbreviated as X n = X (n), n = 0, 1, 2 . . .. The Markov chain  is a sequence of random variables X 1 , X 2 , X 3 . . .. The range of these variables, that is, the set of all their possible values, is called the ''state space'', and the value of X n is the state of time n. The Markov Model BIB002 , BIB001 is a statistical model based on Markov chain, which is widely used in speech recognition, part-of-speech automatic annotation, phonetic conversion, probabilistic grammar and other natural language processing applications. In order to find patterns that change over time, the Markov model attempts to build a process model that can generate patterns. References BIB001 and BIB002 use specific time steps, states, and make Markov assumptions. With these assumptions, this ability to generate a pattern system is a Markov process. A Markov process consists of an initial vector and a state transition matrix. One thing to note about this assumption is that the state transition probability does not change over time. Hidden Markov Model (HMM) BIB004 , BIB003 is a statistical model based on Markov Model, which is used to describe a Markov process with implicit unknown parameters. The difficulty is to determine the implicit parameters of the process from observable parameters, and then use these parameters for further analysis, such as prediction of time series data. For instance, after rolling the dice 10 times, we could get a string of numbers, for example we might get such a string of numbers:1, 4, 5, 3, 3, 1, 6, 2, 4, 5 as shown in Figure 4 . This string of numbers is called the visible state chain. But in HMM, we not only have such a string of visible state chains, but also a chain of implied state chains. In this example, the implicit state chain might be: D5, D3, D2, D3, D4, D6, D1, D5, D1, D2. Gupta and Dhingra BIB005 use HMM to predict the price of stocks. Baba et al. BIB006 argue a data cleaning method based on the HMM, which used to clean RFID data related to geographic location information. In multi-dimensional time series cleaning, HMM has more application space than the single-dimensional cleaning algorithm, because of the correlation between the dimensions. 