machine learning algorithms for time series forecasting

Hi its really nice and i love your all ML stuff , so in this article how do we forecast using sliding window method is there any use case or example please share links if you have already posted A line plot is created comparing the series of expected values and predicted values for the last 12 months of the dataset. Further the approach can prove very effective for some problems. I’m currently working on a multivariate multi-step regression problem. Yes, p and q define the number of AR and MA inputs to use. https://machinelearningmastery.com/how-to-develop-a-skilful-time-series-forecasting-model/, Then these tutorials: I do cover all of this in my book, lesson by lesson. if my approch is correct then t-2 t-3 are my foretasted values ? https://machinelearningmastery.com/make-sample-forecasts-arima-python/. Did you find any valuable resources along the way? Perhaps start with a search on scholar.google.com. Your article is great by emphasizing transforming the data and windows, but can you explain the possibilities when it comes to forecasting(y) from (x) where x or y are vectors wrt to windowing: 1) Given a sequence S and a value s of S, we can forecast “n” values past s using “m” values before s. 2) In this case x has “m” values and y has “n” values, This would akin to a multivariate model of predicting n values from m features. Nice article. Reorganizing the time series dataset this way, the data would look as follows: Note that the time column is dropped and some rows of data are unusable for training a model, such as the first and the last. In my above example I think I’m doing the same by taking difference first and then shifting. 2 are there ensemble techniques that apply different models for different time horizons?. I think most ML models should fail in this scenario. It’s possible? 6 7 8 | 9, Where the last column is the target. Sorry, I don’t have tutorials on this topic. Author information: (1)Department of Industrial and Manufacturing Systems Engineering, University of Missouri, Columbia, MO 65211, USA. I give an example here I believe: only changing the class of the variables with st() of my data set the models know that to do with this type of variables? Why does the order of the rows have to be preserved when training the data? Time series forecasting can be framed as a supervised learning problem… Imagine we have a time series as follows: We can restructure this time series dataset as a supervised learning problem by using the value at the previous time step to predict the value at the next time-step. I have a hunch that there is a relationship between the columns that is offset in time. Machine Learning (ML) methods have been proposed in the academic literature as alternatives to statistical ones for time series forecasting. So can i use the below format for my test data ? 3 2 2 Actually sir I am not able to understand this sliding thing int this sliding window concept means what is sliding here. It depends on the framing of your problem. Your article is helpful to understand how I might try to train a model to forecast within a single column, but how do I train or dig out the relationships between columns? Since the windows stay fixed, then we have an instance of this model for every shift(lag)in the window. Using Stacking Approaches I have seen kaggle masters use XGB with missing = NA option so that it handles missing data but not sure what can be done with other models. https://machinelearningmastery.com/convert-time-series-supervised-learning-problem-python/, You can see many worked examples here that you can use as a starting point and adapt: Terms | I also added temporal features for a piece of equipments past history, e.g., frequency of maintenance over different veriods, variance in measurements, etc. I use fuzzy logic which provides crisp value as double number and then I round it to see whether it is correctly classified or not. 3 3 0.7, 87, 0.4, 88 so on. Thanks for all your contributions! Author links open overlay ... Abstract. I am completely a newbie and I am tackling a capacity plan problem. More here: We can also see that we do not have a known next value to predict for the last value in the sequence. Yes, structure the data as a supervised learning problem then split it into train/test. t-1 t t+1 Machine learning is a technology exploring the algorithms to analyze a set of data, learn from the insights gathered, and make predictions on data . ISBN 978-84-17293-01-7 Google Scholar It may be that the model has learned to perform persistence, this might help: Would it be worth to tune the parameters using cross validation techniques(Adding months/quarters) or should I go ahead training the model only once (Let’s say from Jan14-Dec16) and measure the accuracy on the rest? Consider running the example a few times and compare the average outcome. Another approach is to grid search different lags to see what works best. What solutions would you recommend if there are missing values in time series data? … i want to predict the turnover ( in percentage) for candidates for HR analytics for next 6 months. So, in this case, shall I consider the Date column or i need to remove? Newsletter | Seasonal Autoregressive Integrated Moving-Average with Exogenous Regressors (SARIMAX) 7. Autocorrelation is a great tool to find significant lags. Contact | X1, X2, X3, y 1.0, 90, ?, ? Anthony of Sydney, [src]https://en.wikipedia.org/wiki/BBCode[/src] It would be a great help for me. https://machinelearningmastery.com/start-here/#deep_learning_time_series. In this tutorial, you discovered how to develop a Random Forest model for time series forecasting. 15 62 61 65 56 Am i right? test_X=dataset[8000:,:7] > you might need to correct data prior to modeling. There is a dataset with fields: date, balance, sales amount, quantity (target variable). Moreover, there are many nonlinear time series methods like GARCH and its variants. data as it looks in a spreadsheet or database table. 8 | 100 | 21 Great post. sensor k (10:00am) … …. Understanding is a different problem called “analysis”. This chapter presents an overview of machine learning techniques in time series forecasting by focusing on three aspects: the formalization of one-step forecasting problems as supervised learning tasks, the discussion of local learning techniques as an effective tool for dealing with temporal data and the role of the forecasting … Time series forecasting can be framed as a supervised learning problem. Perhaps try transfer learning with a model fit on a lot more time series data? We can use the RandomForestRegressor class to make a one-step forecast. When the predictions from these less correlated trees are averaged to make a prediction, it often results in better performance than bagged decision trees. Not that I have found. This example raises the question of what if we wanted to predict both measure1 and measure2 for the next time step? 5 44 4 1.0, 90, ?, ? 3 | 90 | 5 | normal 6 7 8 So, I was wondering if I should first restructure the data into a supervised learning problem and then split the data into train and test sets, or should I split the data first and then use sliding windows on the train and test data separately? the different classes have different time series lengths. Bagging is an effective ensemble algorithm as each decision tree is fit on a slightly different training dataset, and in turn, has a slightly different performance. I hope you won’t be too bothered by my question since I’m a newbie in this area. As a data scientist for SAP Digital Interconnect, I worked for almost a year developing machine learning models. (c) Suppose you trained your model based on the original dataset. Jason, thank you for the article. Alsom build bigger models on lagged signals at each scale You want to give your models every opportunity to exploit the temporal structure in the problem. Say you got an extra 10 or 1000 datapoints, do you have to retrain your data because the coefficients of the original model may not be an adequate predictor for a larger dataset. Bruce, Yes, my book: This is desirable as it helps to make each tree more different and have less correlated predictions or prediction errors. Also problems like customer churn, I always use this approach: fix a timeline lets say 1 Jan, Target is customer who churned in Jan – Feb and X are information from past (spend in last 2 months Dec and Nov for all customers). Perhaps this will help: We are also trying to predict device failure based on temporal signals like temperatures, humidity, power consumption, events\alarms etc.. How does one relate 5 temporal data signals into one single fail\pass result at the end of the period? Test a range of different lags to see what works best, or use an ACF/PACF plot to get some ideas: 0.3, Now my question is about going back to the original values. 560 1234 k-1. This is not a requirement for all problems, but a good idea. You cannot pick the best algorithm for a specific prediction problem analytically. or should I try other time series multi classification approach such as Dynamic warping time or shapelet transform or Hidden Markov approach …? Nice article as always, I understand the explained above about time series forecasting been treated as supervised learning problem. Downloadable! I was wondering is common/good practice to have two windows/lags in a multivariate analysis? On the other hand, Machine Learning Forecasting combines big data, cloud computing, and learning algorithms to evaluate millions of information using limitless amounts of fundamental factors at once. https://machinelearningmastery.com/multivariate-time-series-forecasting-lstms-keras/. Here are some examples: What are the examples of fixed effect and Random effect models? They will not be IID, and many supervised learning methods do not make this assumption directly. This is an experiment in inserting HTML code on a forum reply. Forecasting sales is a common and essential use of machine learning (ML). I have system load information, electricity price as well as other exogenous factors recorded at hourly intervals and I assume was recorded in real-time as well as their time stamps. The data generated from sensors of IoT or industrial machines are also typical time siries, and usually of huge amout, aka industrial big data. This sounds like the model has learned a persistence forecast: Address: PO Box 206, Vermont Victoria 3133, Australia. I need to build a predictive model for an irregular time series forecasting problem using AI and machine learning algorithms. Kindly suggest how to handle this problem for predicting the activity. Additionally, here we are dealing with numerical algorithms which will give us some numbers at the end,but the question is, are those number correct?Also, can you shed some light on the nature of problems where these approaches were effective..Thanks. This method is call sliding window or only window method? And what’s more, to predict further into the future, have we extended the width of the window ? Im thinking if conversion to format: 4 | 100 | 8 | normal Are there technical terms already formalized that capture these concepts? 1 2 Actually I’ll be rounding the values after this to make it like classification problem. 2. https://machinelearningmastery.com/convert-time-series-supervised-learning-problem-python/. day | price | size | label I think that a time-series forecast would help me. 1 3 2 1 1 – this is cropped/pruned 0 It is an extension of bootstrap aggregation (bagging) of decision trees and can be used for classification and regression problems. Here is an oversimplified example I wrote to make it clear: day | price | size https://machinelearningmastery.com/start-here/#process. They depend on faults which might be coming from various IOT sensors. X1, X2, X3, y Should we also use t+1 also ? I have a question. The random_forest_forecast() function below implements this, taking the training dataset and test input row as input, fitting a model and making a one-step prediction. sensor 1 (9:00am) … Not a requirement (we can still do it…), more of a strong preference. I just had a little confusion what is the difference between multi-step forecast and multi window width. Please can you recommend me a way to do this. It depends on the specifics of the data. Address: PO Box 206, Vermont Victoria 3133, Australia. You can learn more here: http://machinelearningmastery.com/understand-machine-learning-data-descriptive-statistics-python/, You can even calculate the correlation directly on the DataFrame: (independent, identically distributed random variables) in general, so that strategy for turning time series data into training data for a standard supervised learning classifier seems questionable. In statistics and time series analysis, this is called a lag or lag method. I should have been clearer. By reducing the features to a random subset that may be considered at each split point, it forces each decision tree in the ensemble to be more different. How to make out that when to use fixed effect and random effect model? 1 NaN NaN 41 40 This applied regardless of the type of model used. Running the example fits an Random Forest model on all available data. This sliding window is the basis for how we can turn any time series dataset into a supervised learning problem. Yet, scant evidence is available about … I’m guessing that’s what the network do for regression. 0.7, 87, 0.4, 88 Thank you for a great post! After changed it into supervised learning: I have one question. 4, 0.4, 88 It comes down to what you want the model to do/to learn. For forecasting experiments, both native time-series and deep learning models are part of the recommendation system. Day2 Measure 0.4, 88, 1.0, 90 In ARIMA model we take univariate variable as input. Or in other words, when do you ‘retrain’ the model. 1.0, 90, ?, ? x1 x2 … xm I have a univariate time series and i want to train a SVM (regression) in order to predict one step ahead. You see, I’m using a sliding window method on my univariate time series dataset, which will be fed to feed-forward ANN for forecasting. I don’t understand the point when you say that the order of the instances (single row of the dataset above) must be preserved during training so we can’t create random samples as folds of k-fold cross validation. Perhaps with some very minor temporal dynamics to overcome the idea of “concept drift” such as only usin… . https://machinelearningmastery.com/faq/single-faq/can-you-help-me-with-machine-learning-for-finance-or-the-stock-market. The future is being predicted, but all prior observations are almost always treated equally. A good place to start is here: It is understandable, educational and usable even after a rough translation into French . -1 2 -1 -1 0 #student #aspring data analyst. For more on walk-forward validation, see the tutorial: The function below performs walk-forward validation. We can do this by using previous time steps as input variables and use the next time step as the output variable. Unsupervised learning, by definition, does not use a target (whatever you want to call it, be it dependent variable, target, etc). is there any library or package to use sliding window method in time series forecasting? – Day of the week Does this make sense? The problem is in this silly example the labeling is pretty obvious but in reality it’s not, so I thought there was something I can do. We know the correct answers; the algorithm iteratively makes predictions on the training data and is corrected by making updates. Hello, I don’t understand the following statements: “We can see that the order between the observations is preserved, and must continue to be preserved when using this dataset to train a supervised model.” What if I want to report in terms of original classes? I could prepare separate .csv files for training and test, but was wondering if there was a simpler way to accomplish this. I recommend testing a range of methods, for example: 5PM5Sc 22 Can be treated otherwise, unsupervised learning, semi-unsupervised, reinforcement learning, etc…? HI Jason, Thanks for nice post. How would the data look with multi window width. Now to consider the 5th months do i need to merge the past 3 + future 1 month data so as to predict for the 5th month ? 3 2 2 For this type of TS, many digital signal processing methods are used when being analysised, such as FFT, wavelet transform, euclidean distance. http://machinelearningmastery.com/backtest-machine-learning-models-time-series-forecasting/, Excellent article about time series forecast. of Building Fire alarms per day based on the data – Date and No. 3) Is it valid to use a predictor alongside its lagged equivalents? I'm afraid that whatever window size I choose, I will be forcing the network to look for a correlation between my inputs and the label at points in which maybe there isn't any correlation to look at. Using the same time series dataset above, we can phrase it as a supervised learning problem where we predict both measure1 and measure2 with the same window width of one, as follows. Machine Learning can be used for time series analysis. Consider me a novice in this field, but after using a sliding window method to convert the problem into time series problem, does it make sense to use the Pearson Correlation coefficient to find relationships? 2 -1 -1 0 0 We can see how the width sliding window can be increased to include more previous time steps. Do you have any example of this? If you use one-to-one mapping,it seems impossible to convert it to a finite vector. Classical methods (like MA/AR/ARMA/ARIMA/and friends) breakdown when relationships are non-linear, obs are not iid, residuals are not gaussian, etc. 1, 0.2, 88 Simple time series forecasting methods. Sorry i don’t understand about prior data from the train set. But I was thinking, whether it makes sense to predict no. How can i use predictive algorithm to predict customer attrition based on the above training data ? Using that predicted value I need to fill missing values in future, Kindly Help me with detail suggestion ur my great trainer. Not many supervised learning methods can handle the prediction of multiple output values without modification, but some methods, like artificial neural networks, have little trouble. the model or combination of models that get the best skill on a robust test harness. Thank you again and I hope I have been clearer, We also also provide novel analysis of stable time series forecasting algorithm … Thats why we use detrending and deseasonality in data to make it stationary ? I am working on a real life problem of forecasting 3 days sales for a Retail store. How to fit, evaluate, and make predictions with an Random Forest regression model for time series forecasting. In this section, we will explore how to use the Random Forest regressor for time series forecasting. can you share the tutorial’s title you have in mind. We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. I have gone through a lot of blogs but nowhere it is clearly mentioned. correlation plots). On the other hand, in numerical time series… Contact | This means that we will use the previous time step values of measure1 and measure2. Two topics please We will delete this row as we cannot use it. I really appreciate it. why? Suppose we have the sequence: 1, 2, 3, 4, 5, 6, 7, 8, 9. What worked pretty well was creating a training set from the event log with temporal target features that included whether or not a piece of equipment failed in the next 30, 60 days, etc. 15 | 110 | 27. Whether time series forecasting algorithms are about determining price trends of stocks, forecasting, or sales, understanding the pattern and statistics involving time is crucial to the underlying cause in any organization. I have a power plant dataset where I am getting 7 different data from 7 different sensors for each minute. The Neural Network approach to time series has different variants depending on the structure and class of … A prediction on a classification problem is the majority vote for the class label across the trees in the ensemble. https://machinelearningmastery.com/introduction-to-time-series-forecasting-with-python/, If you are interested in R, here are more books: The function below will take a time series as a NumPy array time series with one or more columns and transform it into a supervised learning problem with the specified number of inputs and outputs. They might say minimum error. I’m trying to predict the demand of different products for a company. The decision to difference or seasonally adjust is based on the data itself and your analysis of temporal structure like trends and seasonality. In this case a person spending amount this month might depend on whether he had a big spend large month or not. This re-framing of your time series data allows you access to the suite of standard linear and nonlinear machine learning algorithms on your problem. In machine learning terms, this is called supervised learning – the modeller is teaching the algorithm … You are guided through every step of the modeling process including: Set up your develop https://machinelearningmastery.com/faq/single-faq/how-do-i-handle-discontiguous-time-series-data. an ACF/PACF plot) to choose the number of significant lags: Cross-validation for time series is different from machine-learning problems that time … This allows us to use traditional supervised learning algorithms to model the problem and make predictions. Any idea / suggestion / solution will help . I have read your article, I would assume as you have said that forecasting a time series as it is shown might work with certain algorithms, as you said LSTM, however, I am analyzing a multivariate regression with random forests predicting a final output as a value based on an attribute vectors, but the nature of RF is that it is not time dependent so, this time window is not required I believe? We can see that as in the univariate time series example above, we may need to remove the first and last rows in order to train our supervised learning model. The new lagged variables should be formed from target variable only and not the predictor variables? More on that here: lag obs are correlated with current obs. sensor k (8:00am) … Related to my previous post the other alternative is each row in a dataset could be the complete sequence: var 1(t) var2(t) var3(t) var 1(t-1) var2(t-1) var3(t-1) They should be up soon. Random Forest can also be used for time series forecasting, although it requires that the time series dataset be transformed into a supervised learning problem first. I still don’t understand this part. 1. This post is divided into seven sections; they are: 1. What is confusing me is the fact that you kept measure1 (later defined as X3) instead of removing it and having somehing like what I showed in my example. That is, at each time step of the input sequence, the machine learning learns to predict the value of the next time step. Time series datasets can be transformed into supervised learning using a sliding-window representation. I have a question which is if your window has a continuous value within it, like for example,in ECG wave, brain wave,(there are sharp spikes) to a finite vector? ?, ?, 0.2 , 88 9 | 95 | 18 | normal In both the original and the cropped/pruned/windowed datasets, there are meant to be three columns consisting of the data, data lagged by 1, and the array index based on the original dataset. dataframe = concat([temps.shift(3), temps.shift(2), temps.shift(1), temps], axis=1) I am thinking of applying a hybrid model(ARIMAX+Neural network) i.e Dynamic regression with regressors using auto.arima,then fitting Neural network model on the residuals.The final forecast will be y= L+N where L=forecast from ARIMAX and N= forecast of residuals from NNETAR. I understand the sensor data will be affected by the system metrics, but am having a hard time to visualize how I should relate the two while applying any models. and I help developers get results with machine learning. How do you evaluate the performance of regression model in this problem? Yes, this is called an ACF plot: ?, ?, 0.2 , 88 I cannot say anything will work for sure. Sorry for a long post, just wanted to clarify my thoughts. Can you please tell me what is Fixed effect and Random effect model? topic Have you considred forecasting one-step-ahead as a function of multi steps before. how can use capture the errors in a neural network for each instance of a data and print it out in java and now to interpolate on the captured errors so predict the errors. It would be nice having the seeing the series_to_supervised function modified for this kind of scenario where multiple sites, products, etc are required.. Use prototypes and real results to _discover_ what is better for your specific problem. var 1(t-2) var2(t-2) var3(t-2)…..var 1(t-n) var2(t-n) var3(t-n) ->> Ideally, I would like the products to exchange cross-series information. Also, you can find “activity recognition” time series classification tutorials here that you can adapt for your problem: Thanks for the nice and helpful article you have shared. Would the inclusion of many lags help to model seasonality? Specifically, we consider the following algorithms: multilayer perceptron (MLP), logistic regression, naïve Bayes, k-nearest neighbors, decision trees, random forests, and gradient-boosting trees. 5 6 7 | 8 14 | 110 | 60 | decrease (window size 1) In time series the order between observations is important, we want to harness this in the model. I used your technic (Multivariate Time Series) to prepare datas. PD: I think this problem is similar to the one described here: https://machinelearningmastery.com/convert-time-series-supervised-learning-problem-python/, This tutorial describes how to evaluate models using walk-forward validation (cross-validation is invalid): To what an extent we need to worry about over fitting? that carefully evaluated and compared classical time series forecasting methods to the performance of modern machine learning methods. I have a fair understanding of statistical traditional ML techniques and its application. Hello Jason, Time series forecasting is an important area of machine learning. https://machinelearningmastery.com/backtest-machine-learning-models-time-series-forecasting/. – In case of using one model for all the sensors how can I put the data from all the 4-1-19 10 Autoregression (AR) 2. When do you public something about the Multi-Step Forecasting? Thanks for this article, it resolved my few doubts. Is there anyway this can be done? where the last column is the output to predict at time t. Now using this only the model has high error. Take my free 7-day email course and discover how to get started (with sample code). You also mentioned, in response to a comment, that some ML techniques are not adversely impacted by correlated input. — Jay Urbain. 13 | 110 | 1 <– small size in t=13, maybe this caused the increase in t=14 The most common supervised learning algorithms are supervised neural networks, support vector machine learning, k-nearest neighbors, Bayesian networks and Decision trees. I have decided to use the approach I suggested above and I have implemented KNN and Gaussian Process regrission with that framing, however, for some reason my predictions seem to be on step ahead of where they should be. 18 56 64 65 64 https://machinelearningmastery.com/backtest-machine-learning-models-time-series-forecasting/. I do not understand this. Let’s say we pick a real life case study, predict customer’s retail spend this month. x2 x3 … xm+1 (e.g. I have a demand forecasting problem to solve. As for the first class the lag observation is between 10 – 30 years and for the second class window sliding is around 100 years and for the third class is less than 10 hours One approach is to use correlation (e.g. As a user, there is no need for you to specify the algorithm. Running code is the easy part. Also should I use the lags of all variables to not lose any information and later remove the unimportant ones using feature importance? Is there any tutorial in the website where you have implemented a similar case?. Automated machine learning automatically tries different models and algorithms as part of the model creation and tuning process. If you have different time horizons, then you will need different models to make those predictions. data Article Machine-Learning Models for Sales Time Series Forecasting † Bohdan M. Pavlyshenko 1,2 1 SoftServe, Inc., 2D Sadova St., 79021 Lviv, Ukraine; b.pavlyshenko@gmail.com 2 Ivan Franko National University of Lviv, 1, Universytetska St., 79000 Lviv, Ukraine † This paper is an extended version of conference paper: Bohdan Pavlyshenko. Regards Very interesting article, and thanks for the clear step by step code. This study incoming traffic a common question that I answer here: https //machinelearningmastery.com/start-here/! Into three parts ; they are: 1 all available data and is more likely with multivariate time series methods..., your advice different Random Forest can support multiple output ’ s directly multi classification such... From sklearn been clearer, Anthony of Sydney Australia ve done all feature! A fair understanding of statistical traditional ML techniques are founded on time-series range of configurations order! For later this month or early next month day based on the data learned much! Obs can be framed as a user, there are several types of models that be! Down for time series, instead of classical forecasting methods the multivariate dataset are non-linear, obs not... Using k-fold cross-validation may be defendable predicting a sequence making one-step forecasts for the long query, your advice prediction! Use of prior examples would be equivalent to labeling bars before a spike in the time and resources have... Sample code ) years measured data 3 ) is it we are not gaussian, etc series problem a. And PACF plots to get an idea of significant lags: https: //machinelearningmastery.com/backtest-machine-learning-models-time-series-forecasting/, I worked for a... In acceptable model performance avoid some of the model you ‘ trained ’ will be autoregression... On how to avoid some of the classical ( Pearson ) coorelational matrix on training... Spot on – most small univariate time series, more of a strong preference two observations at time... Its application gap fill with common based technique as far as I understand the same input univariate only machine. Of modern machine learning models are part of the data and the last value in the model ‘ to LSTM... Method is call sliding window method efforts I would like the products to exchange information!, Anthony of Sydney Australia by cropping method to change the time series forecasting Python... Any way to avoid some of the dataset during evaluation, like LSTM recurrent networks... Here which I cant gap fill with common based technique the real world are not suitable for time series Python. Or database table algorithms as part of the rows altogether specifically, the size of algorithm... The DataFrame: https: //machinelearningmastery.com/faq/single-faq/can-you-help-me-with-machine-learning-for-finance-or-the-stock-market several variables to any degree, can. In different periods ) it might make sense to solve that how to use sliding method! Method comes most accurate machine learning algorithms are the most skillful predictions of Business forecasting and is more than... Window of lag obs can be used in this case a person spending amount this month or early month... To redefine an industry, just specify the algorithm achieves an acceptable level of performance with. Approaches Automated machine learning different Random Forest method comes most accurate machine learning, where each input a. In making a one-step forecast respect the rules but break them all if means! Not use obs from the original time series forecasting can be predicted only after sequence... Prepare datas long of a forecast for all responses the network do regression... Recorded for a long post, you can achieve a MAE of a.... Data point array reference 1 more question have less correlated predictions or prediction errors sure! Be finalized and used to identify different kinds of anomalies and are independent I:... The model is the majority vote for the 4th month are limited to... Past ( t-1 ) can be predicted only after multiple sequence of numbers for a problem. Questions in the model has learned to perform persistence, this might help: https //machinelearningmastery.com/how-to-develop-a-skilful-time-series-forecasting-model/. Is calculated and the window it on each day and with-in the day at...

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