# Solved – LSTM NN produces “shifted” forecast (low quality result)

I am trying to see the power of recurrent neural calculations. I give the NN just one feature, a timeseries datum one step in the past, and predict a current datum. The timeseries is however double-seasonal with considerably long ACF structure (about 64) with additive shorter seasonality for lag 6.

Input timeseries:

Validation result:

You could note it is shifted. I checked my vectors, and they seem OK.

MSE residuals are also quite bad (I expect 0.01 on both train validation thanks to Gaussian noise added with sigma = 0.1):

``> head(x_train) [1]  0.9172955  0.9285578  0.4046166 -0.4144658 -0.3121450  0.3958689 > head(y_train)            [,1] [1,]  0.9285578 [2,]  0.4046166 [3,] -0.4144658 [4,] -0.3121450 [5,]  0.3958689 [6,]  1.5823631 ``

Q: am I doing something wrong in terms of LSTM acrchitecture, or data preparation, or batching?

``library(keras) library(data.table)  # constants  features <- 1 timesteps <- 1  x_diff <- sin(seq(0.1, 100, 0.1)) + sin(seq(1, 1000, 1)) + rnorm(1000, 0, 0.1)  #x_diff <- ((x_diff - min(x_diff)) / (max(x_diff) - min(x_diff)) - 0.5) * 2   # generate  training data  train_list <- list() train_y_list <- list()  for(      i in 1:(length(x_diff) / 2 - timesteps)     ) {      train_list[[i]] <- x_diff[i:(timesteps + i - 1)]      train_y_list[[i]] <- x_diff[timesteps + i] }  x_train <- unlist(train_list) y_train <- unlist(train_y_list)  x_train <- array(x_train, dim = c(length(train_list), timesteps, features)) y_train <- matrix(y_train, ncol = 1)   # generate  validation data  val_list <- list() val_y_list <- list()  for(      i in (length(x_diff) / 2):(length(x_diff) - timesteps) ) {      val_list[[i - length(x_diff) / 2 + 1]] <- x_diff[i:(timesteps + i - 1)]      val_y_list[[i - length(x_diff) / 2 + 1]] <- x_diff[timesteps + i] }  x_val <- unlist(val_list) y_val <- unlist(val_y_list)  x_val <- array(x_val, dim = c(length(val_list), timesteps, features)) y_val <- matrix(y_val, ncol = 1)   ## lstm (stacked) ----------------------------------------------------------  # define and compile model # expected input data shape: (batch_size, timesteps, features)  rm(fx_model)  fx_model <-       keras_model_sequential() %>%       layer_lstm(           units = 32           #, return_sequences = TRUE           , input_shape = c(timesteps, features)           ) %>%       #layer_lstm(units = 16, return_sequences = TRUE) %>%       #layer_lstm(units = 16) %>% # return a single vector dimension 16      #layer_dropout(rate = 0.5) %>%       layer_dense(units = 4, activation = 'tanh') %>%       layer_dense(units = 1, activation = 'linear') %>%       compile(           loss = 'mse',           optimizer = 'RMSprop',           metrics = c('mse')      )   # train  # early_stopping <- #      callback_early_stopping( #           monitor = 'val_loss' #           , patience = 10 #           )  history <-       fx_model %>%       fit(       x_train, y_train, batch_size = 50, epochs = 100, validation_data = list(x_val, y_val) )  plot(history)  ## plot predict  fx_predict <- data.table(      forecast = as.numeric(predict(           fx_model           , x_val      ))      , fact = as.numeric(y_val[, 1])      , timestep = 1:length(x_diff[(length(x_diff) / 2):(length(x_diff) - timesteps)]) )  fx_predict_melt <- melt(fx_predict                         , id.vars = 'timestep'                         , measure.vars = c('fact', 'forecast')                         )  ggplot(      fx_predict_melt[timestep < 301, ]        , aes(x = timestep              , y = value              , group = variable              , color = variable)        ) +      geom_line(           alpha = 0.95           , size = 1      ) +      ggplot_theme ``
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