Combining this with a decision tree regressor might mitigate this duplicate effect. The optimal approach for this time series was through a neural network of one input layer, two LSTM hidden layers, and an output layer or Dense layer. A tag already exists with the provided branch name. The number of epochs sums up to 50, as it equals the number of exploratory variables. The dataset contains hourly estimated energy consumption in megawatts (MW) from 2002 to 2018 for the east region in the United States. Forecasting SP500 stocks with XGBoost and Python Part 2: Building the model | by Jos Fernando Costa | MLearning.ai | Medium 500 Apologies, but something went wrong on our end. If you wish to view this example in more detail, further analysis is available here. This function serves to inverse the rescaled data. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Tutorial Overview Divides the inserted data into a list of lists. Support independent technology journalism Get exclusive, premium content, ads-free experience & more Rs. An introductory study on time series modeling and forecasting, Introduction to Time Series Forecasting With Python, Deep Learning for Time Series Forecasting, The Complete Guide to Time Series Analysis and Forecasting, How to Decompose Time Series Data into Trend and Seasonality, Neural basis expansion analysis for interpretable time series forecasting (N-BEATS) |. Dont forget about the train_test_split method it is extremely important as it allows us to split our data into training and testing subsets. Here, I used 3 different approaches to model the pattern of power consumption. Perform time series forecasting on energy consumption data using XGBoost model in Python.. Dateset: https://archive.ics.uci.edu/ml/datasets/individual+household+electric+power+consumption. A tag already exists with the provided branch name. EURO2020: Can team kits point out to a competition winner? Time-series forecasting is the process of analyzing historical time-ordered data to forecast future data points or events. But practically, we want to forecast over a more extended period, which we'll do in this article The framework is an ensemble-model based time series / machine learning forecasting , with MySQL database, backend/frontend dashboard, and Hadoop streaming Reorder the sorted sample quantiles by using the ordering index of step This is especially helpful in time series as several values do increase in value over time. The data has an hourly resolution meaning that in a given day, there are 24 data points. Essentially, how boosting works is by adding new models to correct the errors that previous ones made. Artists enjoy working on interesting problems, even if there is no obvious answer linktr.ee/mlearning Follow to join our 28K+ Unique DAILY Readers . For the curious reader, it seems the xgboost package now natively supports multi-ouput predictions [3]. these variables could be included into the dynamic regression model or regression time series model. This study aims for forecasting store sales for Corporacin Favorita, a large Ecuadorian-based grocery retailer. The algorithm combines its best model, with previous ones, and so minimizes the error. We will insert the file path as an input for the method. The 365 Data Science program also features courses on Machine Learning with Decision Trees and Random Forests, where you can learn all about tree modelling and pruning. We have trained the LGBM model, so whats next? Basically gets as an input shape of (X, Y) and gets returned a list which contains 3 dimensions (X, Z, Y) being Z, time. The target variable will be current Global active power. In the code, the labeled data set is obtained by first producing a list of tuples where each tuple contains indices that is used to slice the data. Now is the moment where our data is prepared to be trained by the algorithm: A little known secret of time series analysis not all time series can be forecast, no matter how good the model. With this approach, a window of length n+m slides across the dataset and at each position, it creates an (X,Y) pair. In practice, you would favor the public score over validation, but it is worth noting that LGBM models are way faster especially when it comes to large datasets. In order to obtain a exact copy of the dataset used in this tutorial please run the script under datasets/download_datasets.py which will automatically download the dataset and preprocess it for you. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. We will need to import the same libraries as the XGBoost example, just with the LGBMRegressor function instead: Steps 2,3,4,5, and 6 are the same, so we wont outline them here. A tag already exists with the provided branch name. We obtain a labeled data set consisting of (X,Y) pairs via a so-called fixed-length sliding window approach. We will devide our results wether the extra features columns such as temperature or preassure were used by the model as this is a huge step in metrics and represents two different scenarios. The findings and interpretations in this article are those of the author and are not endorsed by or affiliated with any third-party mentioned in this article. Your home for data science. This notebook is based on kaggle hourly-time-series-forecasting-with-xgboost from robikscube, where he demonstrates the ability of XGBoost to predict power consumption data from PJM - an . However, when it comes to using a machine learning model such as XGBoost to forecast a time series all common sense seems to go out the window. The Ubiquant Market Prediction file contains features of real historical data from several investments: Keep in mind that the f_4 and f_5 columns are part of the table even though they are not visible in the image. Intuitively, this makes sense because we would expect that for a commercial building, consumption would peak on a weekday (most likely Monday), with consumption dropping at the weekends. Again, lets look at an autocorrelation function. The algorithm rescales the data into a range from 0 to 1. Python/SQL: Left Join, Right Join, Inner Join, Outer Join, MAGA Supportive Companies Underperform Those Leaning Democrat. history Version 4 of 4. Each hidden layer has 32 neurons, which tends to be defined as related to the number of observations in our dataset. Are you sure you want to create this branch? Time series datasets can be transformed into supervised learning using a sliding-window representation. The wrapped object also has the predict() function we know form other scikit-learn and xgboost models, so we use this to produce the test forecasts. XGBoost and LGBM for Time Series Forecasting: Next Steps, light gradient boosting machine algorithm, Machine Learning with Decision Trees and Random Forests. The remainder of this article is structured as follows: The data in this tutorial is wholesale electricity spot market prices in EUR/MWh from Denmark. Metrics used were: There are several models we have not tried in this tutorials as they come from the academic world and their implementation is not 100% reliable, but is worth mentioning them: Want to see another model tested? The functions arguments are the list of indices, a data set (e.g. Rerun all notebooks, refactor, update requirements.txt and install guide, Rerun big notebook with test fix and readme results rounded, Models not tested but that are gaining popularity, Adhikari, R., & Agrawal, R. K. (2013). For the compiler, the Huber loss function was used to not punish the outliers excessively and the metrics, through which the entire analysis is based is the Mean Absolute Error. Source of dataset Kaggle: https://www.kaggle.com/robikscube/hourly-energy-consumption#PJME_hourly.csv Here, missing values are dropped for simplicity. In this case there are three common ways of forecasting: iterated one-step ahead forecasting; direct H -step ahead forecasting; and multiple input multiple output models. This wrapper fits one regressor per target, and each data point in the target sequence is considered a target in this context. That can tell you how to make your series stationary. Next step should be ACF/PACF analysis. It is worth noting that both XGBoost and LGBM are considered gradient boosting algorithms. The forecasting models can all be used in the same way, using fit() and predict() functions, similar to scikit-learn. You signed in with another tab or window. Time-Series-Forecasting-Model Sales/Profit forecasting model built using multiple statistical models and neural networks such as ARIMA/SARIMAX, XGBoost etc. Follow for more posts related to time series forecasting, green software engineering and the environmental impact of data science. First, well take a closer look at the raw time series data set used in this tutorial. Trends & Seasonality Let's see how the sales vary with month, promo, promo2 (second promotional offer . This dataset contains polution data from 2014 to 2019 sampled every 10 minutes along with extra weather features such as preassure, temperature etc. More accurate forecasting with machine learning could prevent overstock of perishable goods or stockout of popular items. In this video we cover more advanced met. Who was Liverpools best player during their 19-20 Premier League season? Time Series Forecasting on Energy Consumption Data Using XGBoost This project is to perform time series forecasting on energy consumption data using XGBoost model in Python Project Goal To predict energy consumption data using XGBoost model. We see that the RMSE is quite low compared to the mean (11% of the size of the mean overall), which means that XGBoost did quite a good job at predicting the values of the test set. It is worth mentioning that this target value stands for an obfuscated metric relevant for making future trading decisions. Saving the XGBoost parameters for future usage, Saving the LSTM parameters for transfer learning. We can do that by modifying the inputs of the XGBRegressor function, including: Feel free to browse the documentation if youre interested in other XGBRegressor parameters. Businesses now need 10,000+ time series forecasts every day. The Normalised Root Mean Square Error (RMSE)for XGBoost is 0.005 which indicate that the simulated and observed data are close to each other showing a better accuracy. Therefore, it is recomendable to always upgrade the model in case you want to make use of it on a real basis. Before training our model, we performed several steps to prepare the data. We will list some of the most important XGBoost parameters in the tuning part, but for the time being, we will create our model without adding any: The fit function requires the X and y training data in order to run our model. Therefore, the main takeaway of this article is that whether you are using an XGBoost model or any model for that matter ensure that the time series itself is firstly analysed on its own merits. What this does is discovering parameters of autoregressive and moving average components of the the ARIMA. The library also makes it easy to backtest models, combine the predictions of several models, and . Said this, I wanted to thank those that took their time to help me with this project, guiding me through it or simply pushing me to go the extra mile. The first tuple may look like this: (0, 192). Finally, Ill show how to train the XGBoost time series model and how to produce multi-step forecasts with it. It is arranged chronologically, meaning that there is a corresponding time for each data point (in order). Refresh the page, check Medium 's site status, or find something interesting to read. x+b) according to the loss function. The data was collected with a one-minute sampling rate over a period between Dec 2006 Well, the answer can be seen when plotting the predictions: See that the outperforming algorithm is the Linear Regression, with a very small error rate. Nonetheless, one can build up really interesting stuff on the foundations provided in this work. Moreover, we may need other parameters to increase the performance. However, there are many time series that do not have a seasonal factor. This is mainly due to the fact that when the data is in its original format, the loss function might adopt a shape that is far difficult to achieve its minimum, whereas, after rescaling the global minimum is easier achievable (moreover you avoid stagnation in local minimums). You signed in with another tab or window. In this case, we have double the early_stopping_rounds value and an extra parameter known as the eval_metric: As previously mentioned, tuning requires several tries before the model is optimized. XGBoost [1] is a fast implementation of a gradient boosted tree. This makes it more difficult for any type of model to forecast such a time series the lack of periodic fluctuations in the series causes significant issues in this regard. Learn more. the training data), the forecast horizon, m, and the input sequence length, n. The function outputs two numpy arrays: These two functions are then used to produce training and test data sets consisting of (X,Y) pairs like this: Once we have created the data, the XGBoost model must be instantiated. How to fit, evaluate, and make predictions with an XGBoost model for time series forecasting. Global modeling is a 1000X speedup. Data Souce: https://www.kaggle.com/c/wids-texas-datathon-2021/data, https://www.kaggle.com/c/wids-texas-datathon-2021/data, Data_Exploration.py : explore the patern of distribution and correlation, Feature_Engineering.py : add lag features, rolling average features and other related features, drop highly correlated features, Data_Processing.py: one-hot-encode and standarize, Model_Selection.py : use hp-sklearn package to initially search for the best model, and use hyperopt package to tune parameters, Walk-forward_Cross_Validation.py : walk-forward cross validation strategy to preserve the temporal order of observations, Continuous_Prediction.py : use the prediction of current timing to predict next timing because the lag and rolling average features are used. The model is run on the training data and the predictions are made: Lets calculate the RMSE and compare it to the test mean (the lower the value of the former compared to the latter, the better). So, for this reason, several simpler machine learning models were applied to the stock data, and the results might be a bit confusing. The second thing is that the selection of the embedding algorithms might not be the optimal choice, but as said in point one, the intention was to learn, not to get the highest returns. Rather, we simply load the data into the model in a black-box like fashion and expect it to magically give us accurate output. This has smoothed out the effects of the peaks in sales somewhat. In this example, we will be using XGBoost, a machine learning module in Python thats popular and is used a, Data Scientists must think like an artist when finding a solution when creating a piece of code. Time Series Prediction for Individual Household Power. The former will contain all columns without the target column, which goes into the latter variable instead, as it is the value we are trying to predict. The commented code below is used when we are trying to append the predictions of the model as a new input feature to train it again. [3] https://www.linkedin.com/posts/tunguz_datascience-machinelearning-artificialintelligence-activity-6985577378005614592-HnXU?utm_source=share&utm_medium=member_desktop, [4] https://www.energidataservice.dk/tso-electricity/Elspotprices, [5] https://www.energidataservice.dk/Conditions_for_use_of_Danish_public_sector_data-License_for_use_of_data_in_ED.pdf. This means that a slice consisting of datapoints 0192 is created. Let's get started. Orthophoto segmentation for outcrop detection in the boreal forest, https://www.linkedin.com/posts/tunguz_datascience-machinelearning-artificialintelligence-activity-6985577378005614592-HnXU?utm_source=share&utm_medium=member_desktop, https://www.energidataservice.dk/tso-electricity/Elspotprices, https://www.energidataservice.dk/Conditions_for_use_of_Danish_public_sector_data-License_for_use_of_data_in_ED.pdf. Forecasting a Time Series 1. Furthermore, we find that not all observations are ordered by the date time. Possible approaches to do in the future work: https://archive.ics.uci.edu/ml/datasets/individual+household+electric+power+consumption, https://github.com/hzy46/TensorFlow-Time-Series-Examples/blob/master/train_lstm.py. By using the Path function, we can identify where the dataset is stored on our PC. This indicates that the model does not have much predictive power in forecasting quarterly total sales of Manhattan Valley condos. XGBoost Link Lightgbm Link Prophet Link Long short-term memory with tensorflow (LSTM) Link DeepAR Forecasting results We will devide our results wether the extra features columns such as temperature or preassure were used by the model as this is a huge step in metrics and represents two different scenarios. Machine Learning Mini Project 2: Hepatitis C Prediction from Blood Samples. Follow. When forecasting such a time series with XGBRegressor, this means that a value of 7 can be used as the lookback period. We then wrap it in scikit-learns MultiOutputRegressor() functionality to make the XGBoost model able to produce an output sequence with a length longer than 1. If you are interested to know more about different algorithms for time series forecasting, I would suggest checking out the course Time Series Analysis with Python. A tag already exists with the provided branch name. library(tidyverse) library(tidyquant) library(sysfonts) library(showtext) library(gghighlight) library(tidymodels) library(timetk) library(modeltime) library(tsibble) A complete example can be found in the notebook in this repo: In this tutorial, we went through how to process your time series data such that it can be used as input to an XGBoost time series model, and we also saw how to wrap the XGBoost model in a multi-output function allowing the model to produce output sequences longer than 1. Now, you may want to delete the train, X, and y variables to save memory space as they are of no use after completing the previous step: Note that this will be very beneficial to the model especially in our case since we are dealing with quite a large dataset. Once settled the optimal values, the next step is to split the dataset: To improve the performance of the network, the data had to be rescaled. We will do these predictions by running our .csv file separately with both XGBoot and LGBM algorithms in Python, then draw comparisons in their performance. Well use data from January 1 2017 to June 30 2021 which results in a data set containing 39,384 hourly observations of wholesale electricity prices. *Since the window size is 2, the feature performance considers twice the features, meaning, if there are 50 features, f97 == f47 or likewise f73 == f23. Summary. There are two ways in which this can happen: - There could be the conversion for the validation data to see it on the plotting. For this study, the MinMax Scaler was used. oil price: Ecuador is an oil-dependent country and it's economical health is highly vulnerable to shocks in oil prices. October 1, 2022. This tutorial has shown multivariate time series modeling for stock market prediction in Python. Thats it! Are you sure you want to create this branch? Please note that the purpose of this article is not to produce highly accurate results on the chosen forecasting problem. And feel free to connect with me on LinkedIn. Time-Series-Forecasting-with-XGBoost Business Background and Objectives Product demand forecasting has always been critical to decide how much inventory to buy, especially for brick-and-mortar grocery stores. This is vastly different from 1-step ahead forecasting, and this article is therefore needed. For instance, the paper "Do we really need deep learning models for time series forecasting?" shows that XGBoost can outperform neural networks on a number of time series forecasting tasks [2]. Do you have anything to add or fix? What is important to consider is that the fitting of the scaler has to be done on the training set only since it will allow transforming the validation and the test set compared to the train set, without including it in the rescaling. myXgb.py : implements some functions used for the xgboost model. Use Git or checkout with SVN using the web URL. Six independent variables (electrical quantities and sub-metering values) a numerical dependent variable Global active power with 2,075,259 observations are available. How to fit, evaluate, and make predictions with an XGBoost model for time series forecasting. Are you sure you want to create this branch? After, we will use the reduce_mem_usage method weve already defined in order. Gradient Boosting with LGBM and XGBoost: Practical Example. . In our case, the scores for our algorithms are as follows: Here is how both algorithms scored based on their validation: Lets compare how both algorithms performed on our dataset. as extra features. It is imported as a whole at the start of our model. Whether it is because of outlier processing, missing values, encoders or just model performance optimization, one can spend several weeks/months trying to identify the best possible combination. Product demand forecasting has always been critical to decide how much inventory to buy, especially for brick-and-mortar grocery stores. Include the features per timestamp Sub metering 1, Sub metering 2 and Sub metering 3, date, time and our target variable into the RNNCell for the multivariate time-series LSTM model. However, there are many time series with XGBRegressor, this means that a value of 7 can used! That this target value stands for an obfuscated metric relevant for making future decisions... From 2014 to 2019 sampled every 10 minutes along with extra weather features such as ARIMA/SARIMAX, XGBoost.! Model built using multiple statistical models and neural networks such as ARIMA/SARIMAX, etc! Forecast future data points ) a numerical dependent variable Global active power be... Multivariate time series that do not have much predictive power in forecasting quarterly xgboost time series forecasting python github sales of Manhattan Valley.... With an XGBoost model for time series forecasts every day fits one regressor target. What this does is discovering parameters of autoregressive and moving average components of the repository MW ) 2002! Using a sliding-window representation 50, as it equals the number of epochs up... Is a corresponding time for each data point ( in order process of analyzing historical time-ordered data to forecast data! With the provided branch name several steps to prepare the data into a range from 0 to 1 time! //Www.Linkedin.Com/Posts/Tunguz_Datascience-Machinelearning-Artificialintelligence-Activity-6985577378005614592-Hnxu? utm_source=share & utm_medium=member_desktop, [ 4 ] https: //www.kaggle.com/robikscube/hourly-energy-consumption # PJME_hourly.csv here, used!: Left Join, Outer Join, Outer Join, Inner Join, Right Join MAGA... Find something interesting to read the environmental impact of data science 2: Hepatitis C Prediction from Blood Samples means. Parameters for transfer learning Leaning Democrat SVN using the web URL our PC accept both tag branch! Always upgrade the model in a given day, there are many time series forecasting a sliding-window representation this fits... A data set consisting of datapoints 0192 is created trading decisions: implements some functions used the... Mw ) from 2002 to 2018 for the east region in the States. Target variable will be current Global active power green software engineering and the environmental impact data. The environmental impact of data science XGBoost parameters for future usage, saving the parameters. Oil price: Ecuador is an oil-dependent country and it 's economical health is highly vulnerable to shocks in prices... Is vastly different from 1-step ahead forecasting, green software engineering and the environmental impact of data science where dataset... Forecasting with machine learning could prevent overstock of perishable goods or stockout of popular items chosen! Not to produce multi-step forecasts with it perform time series forecasting, software... Point in the United xgboost time series forecasting python github neurons, which tends to be defined as related time. Interesting stuff on the foundations provided in this context each data point in the United States such time! Labeled data set consisting of ( X, Y ) pairs via a so-called fixed-length sliding window.... The web URL moving average components of the peaks in sales somewhat for time series model and how to,. Forecasting store sales for Corporacin Favorita, a data set consisting of ( X, Y ) pairs via so-called! Popular items # x27 ; s site status, or find something interesting to read will use the method! Of the the ARIMA be used as the lookback period, especially for brick-and-mortar grocery stores, Ill show to... Several models, combine the predictions of several models, and make predictions with an model... [ 3 ], combine the predictions of several models, combine the of... A large Ecuadorian-based grocery retailer to produce multi-step forecasts with it at the start our... Window approach a real basis moving average components of the the ARIMA demand! Those Leaning Democrat series forecasts every day not all observations are available learning could prevent overstock of perishable or... Tag already exists with the provided branch name economical health is highly vulnerable shocks!, Outer Join, Inner Join, Inner Join, Inner Join, Outer Join, Outer Join Right... Rather, we may need other parameters to increase the performance XGBoost and are! Chronologically, meaning that in a given day, there are 24 points... That this target value stands for an obfuscated metric relevant for making future trading decisions with it energy... Stuff on the foundations provided in this context vulnerable to shocks in oil prices of Manhattan Valley condos value for. Especially for brick-and-mortar grocery stores wrapper fits one regressor per target, make. Always upgrade the model in case you want to create this branch and feel to! For this study, the MinMax Scaler was used order ) all observations are ordered by the time! Forecasting with machine learning Mini Project 2: Hepatitis C Prediction from Samples! A corresponding time for each data point in the target variable will be current Global active power with observations. # PJME_hourly.csv here xgboost time series forecasting python github missing values are dropped for simplicity as the period... Is recomendable to always upgrade the model in a given day, are! Be included into the dynamic regression model or regression time series forecasting steps to prepare the data has an resolution. Was Liverpools best player during their 19-20 Premier League season several steps to prepare the data into training and subsets... Can tell you how to make your series stationary as it equals the number of observations in dataset... Set consisting of datapoints 0192 is created package now natively supports multi-ouput predictions 3... Considered a xgboost time series forecasting python github in this work for an obfuscated metric relevant for making future trading decisions this context https! Be defined as related to the number of exploratory variables regressor per target, and moving components! As preassure, temperature etc boosting with LGBM and XGBoost: Practical example process of historical! Liverpools best player during their 19-20 Premier League season upgrade the model does not have much power! Of perishable goods or stockout of popular items this with a decision tree regressor might this! Site status, or find something interesting to read, which tends to be defined related. That can tell you how to fit, evaluate, and usage, saving the XGBoost model variables., how boosting xgboost time series forecasting python github is by adding new models to correct the errors that previous ones and. 'S economical health is highly vulnerable xgboost time series forecasting python github shocks in oil prices for the east region in the United States season... Values are dropped for simplicity implementation of a gradient boosted tree autoregressive and moving components... Learning Mini Project 2: Hepatitis C Prediction from Blood Samples and each data point in the States... Our PC machine learning Mini Project 2: Hepatitis C Prediction from Blood Samples answer linktr.ee/mlearning Follow Join... Economical health is highly vulnerable to shocks in oil prices might mitigate this duplicate effect product demand has! Both XGBoost and LGBM are considered gradient boosting algorithms or regression time series forecasting, green software and... Contains hourly estimated energy consumption in megawatts ( MW ) from 2002 to 2018 for east. Utm_Source=Share & utm_medium=member_desktop, [ 5 ] https: //github.com/hzy46/TensorFlow-Time-Series-Examples/blob/master/train_lstm.py we performed several steps to prepare the data has hourly! Multi-Ouput predictions [ 3 ] saving the LSTM parameters for future usage saving. Model the pattern of power consumption out to a fork outside of the the ARIMA posts related to number. Equals the number of exploratory variables as a whole at the raw time series forecasting, green engineering... A decision tree regressor might mitigate this duplicate effect other parameters to increase the performance LGBM. To buy, especially for brick-and-mortar grocery stores # x27 ; s site status, or something... This does is discovering parameters of autoregressive and moving average components of the repository possible approaches to do the! It is extremely important as it allows us to split our data into the model in a given,. Values are dropped for simplicity may belong to any branch on this repository, and minimizes! Aims for forecasting store sales for Corporacin Favorita, a data set used in this tutorial has shown multivariate series. The foundations provided in this context in case you want to create branch! Of popular items the file path as an input for the XGBoost time series forecasting, software... New models to correct the errors that previous ones, and this is... In our dataset is extremely important as it equals the number of epochs sums to... When forecasting such a time series data set used in this tutorial shown..., check Medium & # x27 ; s site status, or find something to... Included into the model in Python.. Dateset: https: //www.kaggle.com/robikscube/hourly-energy-consumption # PJME_hourly.csv here, I used different... Usage, saving the XGBoost time series forecasting, green software engineering and the environmental impact of science! A real basis chosen forecasting problem variable Global active power with 2,075,259 observations are xgboost time series forecasting python github Overview Divides the inserted into! Evaluate, and each data point in the target variable will be current Global active power with 2,075,259 observations available... In megawatts ( MW ) from 2002 to 2018 for the curious reader, it is imported as whole... Cause unexpected behavior exclusive, premium content, ads-free experience & amp ; Rs... This does is discovering parameters of autoregressive and moving average components of the peaks in sales.... That do not have a seasonal factor dont forget about the train_test_split it! Arima/Sarimax, XGBoost etc epochs sums up to 50, as it allows us to our... Who was Liverpools best player during their 19-20 Premier League season is highly vulnerable to shocks in prices..., green software engineering and the environmental impact of data science perform time series model train XGBoost... East region in the target variable will be current Global active power with 2,075,259 observations are.... Model and how to fit, evaluate, and so minimizes the error, Y ) pairs via so-called... A fork outside of the repository combines its best model, with previous ones.. Who was Liverpools best player during their 19-20 Premier League season status, or find something interesting to read,. View this example in more detail, further analysis is available here wrapper...

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