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What is the autoregressive model in TensorFlow? I believe many inexperienced people don't know what to do about it. Therefore, this paper summarizes the causes and solutions of the problem. Through this article, I hope you can solve this problem.

The really cool thing about autoregressive models is that they are similar to open-loop feedback systems, a control system. The objective functions of these models are buried under some heavy, almost absurd mathematics, but I finally found the skill to build autoregressive models by searching Wikipedia. You can summarize the technique in the following equation by inserting (1) into (2) to create an expression (3). As a result of this transformation, the intercept is limited to a certain proportion of autoregressive weights. You can use TensorFlow to optimize this objective function. Please check the notebook for this post here.

The following code block shows how to combine weights and data in the TensorFlow of this model. The data are shaped into tuples of input and output, and the observation results are divided into training and test data sets. The training data set is shuffled. Random micro batches were used in each period, of which 50% of the training observations were made. A gradient descent optimizer with a very small learning rate is used to prevent overfitting.

Hidden_layer_1 = 1

Weights1 = tf.Variable (tf.random_normal ((X_train.shape [1], hidden_layer_1), stddev=0.01,dtype='float32'))

B1 = tf.Variable (tf.zeros ((1 dtype='float32')

Input_X = tf.placeholder ('float32', (None,X_ room.shape [1]))

Input_y = tf.placeholder ('float32', (None,1))

Predicted_out = tf.add (tf.matmul (input_X,weights1), tf.reduce_sum (b1*weights1))

Loss = tf.reduce_sum (tf.square (predicted_out-input_y))

Optimizer = tf.train.AdamOptimizer (learning_rate=0.00001) .minimize (loss)

An autoregressive model is established using the daily minimum temperature in the Melbourne time series in Australia. The time series data does not need much preprocessing, that is, only the Nano value is interpolated. There are a total of ~ 3500 observations in the clean data set, 80% of which are used for training.

The automatic correlation graph shown below is created by using the correlation function of numpy, by using the second half of the correlation. Then use the signal.detrend function of scipy to remove the results. The following chart has the following lagging peaks: [170, 356, 528, 720, 897, 1079, 1257, 1455, 1622]. The strongest correlation is extracted by obtaining at least two standard deviations from the average correlation. In the following figure, the strong correlation lag can be seen in green.

The input data is subset to include the elimination of weak correlation lag. This improves the quality of input data by selecting only highly relevant lag variables. These highly correlated lag observations are extracted into a matrix of observations for each target.

Snowballed Autoregressive Time Series

When a decision needs to be made in advance, the prediction of time series may be preferable. You can create predictions by predicting "snowball" in autoregressive models. Even if the actual time series has a constant variance, the variance of snowball time series will increase with the passage of time. Inappropriate models may become unstable and change over time. However, this increased variance is usually due to the fact that the snowball time series is higher or lower than the actual trend of the time series. This seems to be the human factor of using the open-loop system, rather than shutting down the system used in the electrical control system. In order to test the randomness of the direction of trend components, 1000 small batch training models are used. The results of the model save the last 900 periods and generate a snowball time series for each period.

The snowball time series divided by time is shown in the figure above. The randomness of the trend is tested by checking whether the average error of each snowball time series is higher or lower than zero. Over the past 900600 and 300th periods, the snowball time series of positive trends has roughly doubled the number of negative trends. The average error distribution by time is shown in the following figure.

The average seems to be centered around 1, which means that most snowball time series overpredict the actual value. The distribution also seems to tilt slightly. However, it turns out that the snowball effect is not significant for medium-range predictions. One possible solution to the noise problem is to average the N in the snowball prediction.

The last N lag components are used as predictors in the autoregressive model. When the last 30 models over the past 30 periods were integrated on average, about 51% of the changes in test data were explained. The second figure above shows the r square of the standard deviation from the average of the snowball time series. We can see that for the positive standard deviation (+ 1 meme + 2 meme + 3), the r square of the negative square (- 1 memmel 2 meme 3) is slightly more, which indicates that the model may be overpredicted.

Actual observation and prediction

Instead of predicting the next time step, we can give the last N values of each observation in the test data set. The predicted time series is shown below. When average integration came from the last 30 periods of the TensorFlow optimizer, it explained about 58% of the changes in the test data, 7% more than the snowball forecast. Interestingly, the "average of the average and the standard deviation" indicates that the model may be overpredicted.

After reading the above, have you mastered the method of autoregressive model in TensorFlow? If you want to learn more skills or want to know more about it, you are welcome to follow the industry information channel, thank you for reading!

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