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      "body": "How did you justify your cryptocurrency decisions over the past year? It's probably a good time to think about how you make decisions.\n\nThis post talks about randomness in markets, and the techniques for dealing with that randomness, as well as the important consideration of correlation between the prices of different assets while making decisions.\n\n\n### Random Walks and Randomness in markets\nPerhaps the most striking thing that happened to me to change my understanding of financial markets was thinking about random walks. When I was looking at the R statistics language, one of the exercises was to simulate a random walk and plot the result. To do this you pick say 100 numbers at random from some distribution and then plot the total after adding each number.\n![randomwalk.png](https://cdn.steemitimages.com/DQmZmGRCagspFAjRVYTSmGYMAvuRSnJRme9dGyo1RdWyVKS/randomwalk.png)\nIf you take anything away from this post it should be this: **It is impossible to distinguish a plot of the price of a currency from the plot of a random walk** and from a mathematical point of view, if two things are indistinguishable then they may as well be the same. This plot has been produced just by picking numbers from a standard normal distribution and then adding them up, but if you look at from technical analysis point of view, maybe you'd think that judging by this chart its a good idea to buy some of this currency. Maybe you can even see some [Elliot waves](https://en.wikipedia.org/wiki/Elliott_wave_principle) This raises two questions: Thinking of markets as random walks, how on earth do people actually make money by looking at charts? and is it possible to study the randomness of the different cryptocurrencies to make forecasts? \n\nThe answer to the first question is that people generally don't. With cryptocurrencies in 2017,iIt's generally accepted that lots of people made money because of a huge speculative interest. As long as the decision was to end up with a holding of cryptocurrency,  the value would increase since lots of people were finding out about cryptocurrencies. If one was making money with a dodgy decision making process then one wouldn't feel the need to question those decisions, and instead believe that they were making money because of their currency portfolio decisions. With normal stock broker accounts people generally lose money to such an extent that the brokers [don't even bother properly buying the stocks that their customers decide to buy and in many cases set their investments to do the opposite of what their customers do.](https://youtu.be/L7G0OfJUON8?t=40m6s)\n\nThe answer to the second question is yes, but it is very complicated. The best way to model the currency price movements is as a random walk, but the random variable at each time step (as in the random number that determines what to add to the total) depends on what has happened to the price in the past. [Time series analysis](https://en.wikipedia.org/wiki/Time_series#Analysis) is the study of such processes. Note that this is very different to the chart reading that can be found on YouTube and steemit as predictions can be made with quantitative confidence intervals and expected price increases. Neural networks and other machine learning techniques (see my other posts) also offer ways of predicting how currencies will evolve through time by learning the expected change in price given the previous price changes. It is important to remember that all these techniques use the fact  that fundamentally the markets are random and the best you can do is predict the expected price movements and assess how likely these price movements are going to be.  \n\n### Correlations in the prices of different assets\nPredictions of the future prices of cryptocurrencies (and of other markets) are made all the more complicated when one considers correlations between the different currencies. For example, if bitcoin increases in price, then it it likely that many other cryptocurrencies will also increase in price either at the same time or with some positive or negative delay on the bitcoin price.  This is definitely something to consider when selecting cryptocurrencies to form a portfolio with since if, for example, two currencies share the same gains then is there any point in selecting one over the other? If two currencies are negatively correlated (ie one goes up in price when the other goes down in price) then how do you decide how much of each to buy, given a prediction and confidence of that prediction? This is an area of mathematics / economics called portfolio theory, and it is quite a large field. If you make your decisions based of predictions from separate sources then your decisions are likely not to be optimal from a risk minimising point of view because each prediction is likely to be heavily correlated. To make decisions about a portfolio to make money you need to be able to consider the correlations between different currencies and be able to judge how likely it is that your predictions will be realised.\n\n### Where to go from here\nTo make money, generally you need to act rationally. If you don't have any grounds for owning the cryptocurrencies that you do, then perhaps it is best to either invest in some sort of fund run by people who can prove to you that they know what is going on, or spend a lot of time researching the things mentioned above - ways of making predictions and portfolio theory. It is also possible to change your strategy from investing based on the prices of currencies to the projects themselves, but it is incredibly hard for your decisions not to be influenced by the current price of the currency. In any case, making sure all future financial decisions are completely justified, and not based on the output of a random number generator is an excellent way to increase the likelihood of your investments doing well.\n\nI plan to write more about the process of making sensible decisions, so if you are interested then be sure to follow me. If you have any questions then don't hesitate to post them in the replies.",
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      "body": "Code available on [github]()\n### Introduction\nI started developing neural networks to predict BTC price moves about two weeks ago. [My previous post](https://steemit.com/bitcoin/@homes/financial-modeling-blog-1-btc-price-prediction-using-basic-neural-networks) looked at my initial thoughts and attempts using a simple neural network. Since then I've implemented Tensorflow's [LSTM](https://www.tensorflow.org/versions/r1.0/api_docs/python/tf/contrib/rnn/LSTMCell) and [RNN](https://www.tensorflow.org/versions/r1.0/api_docs/python/tf/contrib/rnn/static_rnn) (Recurrent Neural Network) modules to generate more accurate predictions, but this time using hourly data.\n### How the RNN (with LSTM cell) works\nThe RNN takes the previous week's hourly trading data (average price and volume for each hour) and outputs a prediction for the price and volume of the next hour. This is then fed back into the network 24 times to predict the daily price and volume. The R in RNN stands for recurrent meaning that the prediction for each hour is calculated by the network being given the previous hour's data and also information from the network its self after it processed the hour before's data. RNN's  are quite complicated, but it is quite straight forward to use Tensorflow's built in classes.\n### Implementation\nI decided to refactor the code from before, wrapping the Tensorflow code in a class called [TimeSeriesForcaster](https://github.com/alfredholmes/shortterm_rnn/blob/master/rnn.py) which makes writing the code that uses the RNN much simpler and also creating a separate [functions](https://github.com/alfredholmes/shortterm_rnn/blob/master/functions.py) file to hold all the data manipulation (reading files, scaling data etc) functions cleaned up the code a lot. This means its quite straightforward to write scripts to use the RNN, where as before everything was done in one file and so altering what the NN predicted was difficult as I didn't want to lose functionality when editing the code. \n### Results - Trading strategy\n![NN_Trading_Strategy.png](https://steemitimages.com/DQmS1fpq3X8smophF93HRWF8R7Jmwje33GvS3vyEpuWPqcA/NN_Trading_Strategy.png)\nThe neural network seems to do a good job of predicting daily changes in price. The above price shows the value of a $1000 investment over period of 240 days if once a day I was to run the neural network, see if the price will increase and then buy / sell based on that predicted price. This is just a basic last minute test to evaluate the neural network, and it seems to do well on average, especially around the ATH. The period on the graph is the previous 200 days. The neural network was not trained on this data. If this was used with decent technical analysis then I am confident that the RNN could be used effectively to increase one's bitcoin investments substantially over the period of a year. The simulation does not account for trading fees.\n### Things to work on\nThe python code uses the RNN and the assumption that it's errors are normally distributed to generate a distribution of possible prices. This information is much more detailed than whether the price will increase or decrease and so could be used to develop a more complicated strategy - in particular, if I was able to forecast other the prices of other crypto currencies, techniques in artificial intelligence and genetic programming could be used to train agents to make better than human trading decisions.",
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      "body": "Code available on [github]()\n### Introduction\nI started developing neural networks to predict BTC price moves about two weeks ago. [My previous post](https://steemit.com/bitcoin/@homes/financial-modeling-blog-1-btc-price-prediction-using-basic-neural-networks) looked at my initial thoughts and attempts using a simple neural network. Since then I've implemented Tensorflow's [LSTM](https://www.tensorflow.org/versions/r1.0/api_docs/python/tf/contrib/rnn/LSTMCell) and [RNN](https://www.tensorflow.org/versions/r1.0/api_docs/python/tf/contrib/rnn/static_rnn) (Recurrent Neural Network) modules to generate more accurate predictions, but this time using hourly data.\n### How the RNN (with LSTM cell) works\nThe RNN takes the previous week's hourly trading data (average price and volume for each hour) and outputs a prediction for the price and volume of the next hour. This is then fed back into the network 24 times to predict the daily price and volume. The R in RNN stands for recurrent meaning that the prediction for each hour is calculated by the network being given the previous hour's data and also information from the network its self after it processed the hour before's data. RNN's  are quite complicated, but it is quite straight forward to use Tensorflow's built in classes.\n### Implementation\nI decided to refactor the code from before, wrapping the Tensorflow code in a class called [TimeSeriesForcaster](https://github.com/alfredholmes/shortterm_rnn/blob/master/rnn.py) which makes writing the code that uses the RNN much simpler and also creating a separate [functions](https://github.com/alfredholmes/shortterm_rnn/blob/master/functions.py) file to hold all the data manipulation (reading files, scaling data etc) functions cleaned up the code a lot. This means its quite straightforward to write scripts to use the RNN, where as before everything was done in one file and so altering what the NN predicted was difficult as I didn't want to lose functionality when editing the code. \n### Results - Trading strategy\n![NN_Trading_Strategy.png](https://steemitimages.com/DQmS1fpq3X8smophF93HRWF8R7Jmwje33GvS3vyEpuWPqcA/NN_Trading_Strategy.png)\nThe neural network seems to do a good job of predicting daily changes in price. The above price shows the value of a $1000 investment over period of 240 days if once a day I was to run the neural network, see if the price will increase and then buy / sell based on that predicted price. This is just a basic last minute test to evaluate the neural network, and it seems to do well on average, especially around the ATH. The period on the graph is the previous 200 days. The neural network was not trained on this data. If this was used with decent technical analysis then I am confident that the RNN could be used effectively to increase one's bitcoin investments substantially over the period of a year. The simulation does not account for trading fees.\n### Things to work on\nThe python code uses the RNN and the assumption that it's errors are normally distributed to generate a distribution of possible prices. This information is much more detailed than whether the price will increase or decrease and so could be used to develop a more complicated strategy - in particular, if I was able to forecast other the prices of other crypto currencies, techniques in artificial intelligence and genetic programming could be used to train agents to make better than human trading decisions.",
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      "body": "Code available on [github]()\n### Introduction\nI started developing neural networks to predict BTC price moves about two weeks ago. [My previous post](https://steemit.com/bitcoin/@homes/financial-modeling-blog-1-btc-price-prediction-using-basic-neural-networks) looked at my initial thoughts and attempts using a simple neural network. Since then I've implemented Tensorflow's [LSTM](https://www.tensorflow.org/versions/r1.0/api_docs/python/tf/contrib/rnn/LSTMCell) and [RNN](https://www.tensorflow.org/versions/r1.0/api_docs/python/tf/contrib/rnn/static_rnn) (Recurrent Neural Network) modules to generate more accurate predictions, but this time using hourly data.\n### How the RNN (with LSTM cell) works\nThe RNN takes the previous week's hourly trading data (average price and volume for each hour) and outputs a prediction for the price and volume of the next hour. This is then fed back into the network 24 times to predict the daily price and volume. The R in RNN stands for recurrent meaning that the prediction for each hour is calculated by the network being given the previous hour's data and also information from the network its self after it processed the hour before's data. RNN's  are quite complicated, but it is quite straight forward to use Tensorflow's built in classes.\n### Implementation\nI decided to refactor the code from before, wrapping the Tensorflow code in a class called [TimeSeriesForcaster](https://github.com/alfredholmes/shortterm_rnn/blob/master/rnn.py) which makes writing the code that uses the RNN much simpler and also creating a separate [functions](https://github.com/alfredholmes/shortterm_rnn/blob/master/functions.py) file to hold all the data manipulation (reading files, scaling data etc) functions cleaned up the code a lot. This means its quite straightforward to write scripts to use the RNN, where as before everything was done in one file and so altering what the NN predicted was difficult as I didn't want to lose functionality when editing the code. \n### Results - Trading strategy\n![NN_Trading_Strategy.png](https://steemitimages.com/DQmS1fpq3X8smophF93HRWF8R7Jmwje33GvS3vyEpuWPqcA/NN_Trading_Strategy.png)\nThe neural network seems to do a good job of predicting daily changes in price. The above price shows the value of a $1000 investment over period of 240 days if once a day I was to run the neural network, see if the price will increase and then buy / sell based on that predicted price. This is just a basic last minute test to evaluate the neural network, and it seems to do well on average, especially around the ATH. The period on the graph is the previous 200 days. The neural network was not trained on this data. If this was used with decent technical analysis then I am confident that the RNN could be used effectively to increase one's bitcoin investments substantially over the period of a year. The simulation does not account for trading fees.\n### Things to work on\nThe python code uses the RNN and the assumption that it's errors are normally distributed to generate a distribution of possible prices. This information is much more detailed than whether the price will increase or decrease and so could be used to develop a more complicated strategy - in particular, if I was able to forecast other the prices of other crypto currencies, techniques in artificial intelligence and genetic programming could be used to train agents to make better than human trading decisions.",
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      "body": "Code available on [Githhub](https://github.com/alfredholmes/tensorflow-btc-predictions)\n### Introduction\nRecently I've taken an interest in financial markets as complex mathematical systems and contemporary methods for predictions, forecasts and gathering data on how particular markets are behaving.  This is a blog post summarising the previous few days of work where I developed a basic neural network to predict the next day's bitcoin price based on the previous 10 days using Google's tensorflow library.\n\nIt is my goal over the comming months to develop a range of computational modelling techniques, in order to forecast the price, test the markets stability and asses the probabilities associated with financial forecasts.  I plan on posting my findings on this site.\n\n### An Impressive Graph\nRed line: prediction. Blue line: actual price.\n![NNoutput.png](https://steemitimages.com/DQmYvwcx5vu1AncDvndQeMTJtHJS1TfUFhWu4Aac8P4dno4/NNoutput.png)\nI was quite surprised by the accuracy of the neural network's prediction, especially over period when the BTC price approached $20000 as this was rather abnormal behaviour even for bitcoin. The network was trained on BTC-USD price data from Coinbase ([source](http://api.bitcoincharts.com/v1/csv/)) from when Coinbase first started until about a year and a half ago, and then tested against price data from the past year and a half. The data was just a list of transactions that happened on the Coinbase exchange (perhaps actually GDAX) and so I wrote [aquire.py](https://github.com/alfredholmes/tensorflow-btc-predictions/blob/master/aquire.py) to sort through and find the daily volume and average price. The network averages about .7% error on the training data set.  In order to be able to use the neural network to predict the price that data needs to be normalised so that it is between 0 and 1, which is achieved by\n![ql_82d52cccb1cf064951df5e6108d2d5d4_l3.png](https://steemitimages.com/DQmTvGSArxEUwixYroRUL7uLzcQbT7T5CjnUY86KcXxSTMq/ql_82d52cccb1cf064951df5e6108d2d5d4_l3.png)\nwhere r is the range and m is the minimum price, p is the price and a is the data that is given to the network. In doing this the network is unable to tell the real size of the price, only the relative changes.\n### Taking closer look\n![closeupbtc.png](https://steemitimages.com/DQmPW6pAdvyYHWncmGK42f3FQosZyfmJdsHdb4okYDWMFJY/closeupbtc.png)\nThis is the network's prediction for the price action when bitcoin reached it's current all time high (as of April 2018). Unfortunately this shows a rather large flaw in the output. When there is extreme price action, the output is heavily reliant on the previous day's price and is only a little bit better than just predicting that tomorrow's price will be about the same as today's price. The main use of this neural network would have to be: 'assuming nothing that big will happen with bitcoin's price, this is what will probably happen'. If one was to try and forecast using this neural network around the 21st day mark then the network really has no idea when the price will stop rising. In order to get a better grasp on these situations, the network needs more information, perhaps in the form of the number of active users trading bitcoin, the number of new users entering the market and the volume. I'll discuss this more in the next blog where I'll be looking at recurrent neural networks, as in this form giving this data to the neural network is easier.\n### Attempting forecasting\nGiven that the neural network's error is about 0.7% and assuming a normal distribution of errors, in theory I should be able to create a distribution of possible future prices by making a prediction, giving it a random bit of error and then feeding that result back into the neural network to predict the next day. Here is a graph of an example prediction, taken from around November time. \n![extrapolation.png](https://steemitimages.com/DQmSihmamj3sie1W56khHbyZ6Ggusw6zCMD3hG3rgvYgKCH/extrapolation.png)\nAs you can see the network does an alright job predicting the price for the first 4 or so days (this is a rather calm period, the network isn't capable of knowing whether large price movements are likely). After 4 days however the neural network just seems to converge on a price that is around that of the input as I suppose this is the general case when predicting the next days value, especially as the network was trained on old (pre 2017 data).\n\nOver the coming weeks I'll investigate other techniques to model the price action of bitcoin and the interaction of other cryptocurrencies.",
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      "body": "Code available on [Githhub](https://github.com/alfredholmes/tensorflow-btc-predictions)\n### Introduction\nRecently I've taken an interest in financial markets as complex mathematical systems and contemporary methods for predictions, forecasts and gathering data on how particular markets are behaving.  This is a blog post summarising the previous few days of work where I developed a basic neural network to predict the next day's bitcoin price based on the previous 10 days using Google's tensorflow library.\n\nIt is my goal over the comming months to develop a range of computational modelling techniques, in order to forecast the price, test the markets stability and asses the probabilities associated with financial forecasts.  I plan on posting my findings on this site.\n\n### An Impressive Graph\nRed line: prediction. Blue line: actual price.\n![NNoutput.png](https://steemitimages.com/DQmYvwcx5vu1AncDvndQeMTJtHJS1TfUFhWu4Aac8P4dno4/NNoutput.png)\nI was quite surprised by the accuracy of the neural network's prediction, especially over period when the BTC price approached $20000 as this was rather abnormal behaviour even for bitcoin. The network was trained on BTC-USD price data from Coinbase ([source](http://api.bitcoincharts.com/v1/csv/)) from when Coinbase first started until about a year and a half ago, and then tested against price data from the past year and a half. The data was just a list of transactions that happened on the Coinbase exchange (perhaps actually GDAX) and so I wrote [aquire.py](https://github.com/alfredholmes/tensorflow-btc-predictions/blob/master/aquire.py) to sort through and find the daily volume and average price. The network averages about .7% error on the training data set.  In order to be able to use the neural network to predict the price that data needs to be normalised so that it is between 0 and 1, which is achieved by\n![ql_82d52cccb1cf064951df5e6108d2d5d4_l3.png](https://steemitimages.com/DQmTvGSArxEUwixYroRUL7uLzcQbT7T5CjnUY86KcXxSTMq/ql_82d52cccb1cf064951df5e6108d2d5d4_l3.png)\nwhere r is the range and m is the minimum price, p is the price and a is the data that is given to the network. In doing this the network is unable to tell the real size of the price, only the relative changes.\n### Taking closer look\n![closeupbtc.png](https://steemitimages.com/DQmPW6pAdvyYHWncmGK42f3FQosZyfmJdsHdb4okYDWMFJY/closeupbtc.png)\nThis is the network's prediction for the price action when bitcoin reached it's current all time high (as of April 2018). Unfortunately this shows a rather large flaw in the output. When there is extreme price action, the output is heavily reliant on the previous day's price and is only a little bit better than just predicting that tomorrow's price will be about the same as today's price. The main use of this neural network would have to be: 'assuming nothing that big will happen with bitcoin's price, this is what will probably happen'. If one was to try and forecast using this neural network around the 21st day mark then the network really has no idea when the price will stop rising. In order to get a better grasp on these situations, the network needs more information, perhaps in the form of the number of active users trading bitcoin, the number of new users entering the market and the volume. I'll discuss this more in the next blog where I'll be looking at recurrent neural networks, as in this form giving this data to the neural network is easier.\n### Attempting forecasting\nGiven that the neural network's error is about 0.7% and assuming a normal distribution of errors, in theory I should be able to create a distribution of possible future prices by making a prediction, giving it a random bit of error and then feeding that result back into the neural network to predict the next day. Here is a graph of an example prediction, taken from around November time. \n![extrapolation.png](https://steemitimages.com/DQmSihmamj3sie1W56khHbyZ6Ggusw6zCMD3hG3rgvYgKCH/extrapolation.png)\nAs you can see the network does an alright job predicting the price for the first 4 or so days (this is a rather calm period, the network isn't capable of knowing whether large price movements are likely). After 4 days however the neural network just seems to converge on a price that is around that of the input as I suppose this is the general case when predicting the next days value, especially as the network was trained on old (pre 2017 data).\n\nOver the coming weeks I'll investigate other techniques to model the price action of bitcoin and the interaction of other cryptocurrencies.",
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