Forecasting Modeling for Bitcoin Prices

The models will be updated every Sunday.

Description of the data:

Date 24h Average 12h Average Last Volume (BTC)
Min. :2014-04-15 Min. : 222 Min. : 212 Min. : 201.6 Min. : 34.3
1st Qu.:2015-03-25 1st Qu.: 379 1st Qu.: 377 1st Qu.: 396.1 1st Qu.: 599.5
Median :2016-03-20 Median : 622 Median : 621 Median : 633.0 Median :1168.4
Mean :2016-02-28 Mean : 10779 Mean : 12202 Mean : 1593.5 Mean :1315.0
3rd Qu.:2017-01-27 3rd Qu.: 1099 3rd Qu.: 1080 3rd Qu.: 1256.0 3rd Qu.:1943.8
Max. :2017-12-11 Max. :11620677 Max. :13386698 Max. :43559.7 Max. :3805.7

Forecasting Models used:

1. Autoregressive Integrated Moving Average Model (ARIMA)

2. Regression Model (REG)

3. Weighted Average Model using Mean Absolute Percentage Error MAPE (WA)

4. Automatic ARIMA Model

The Best Forecasting Model is:

ARIMA Model

The best model is the fitted ARIMA model. It is a MA(0,1,1) model on the log log transformed values of the original data. Forecasted values and 95 percent confidence intervals of the next five observations are:

  MA_lower_95percentCL MA_forecasted_value MA_upper_95percentCL
1 10529 18251 32689
2 10458 18316 33184
3 10391 18381 33679
4 10325 18446 34177
5 10262 18511 34676

Model equation and details:

EstimateSEt.valuep.value
ma1 -0.8054 0.0170 -47.4478 0.0000
constant 0.0004 0.0002 2.1638 0.0307

sigma^2 estimated as: 0.0008666539729651
log likelihood: 2588.36173022797
aic: -5170.72346045594

Errors of the MA model:

mean error (ME) 8259.58189557301
mean absolute error (MAE) 8390.18722776554
mean squared error (MSE) 151121022.120531
mean percentage error (MPE) 32.5866270742033
mean absolute percentage error (MAPE) 33.8272228416508

Plot of data together with the forecasted values in red:

The next best forecasting model is:

Automatic ARIMA Model

The following model is the Automatic ARIMA model. Forecasted values and 95 percent confidence intervals of the next five observations are:

  AUTO_lower_95percentCL AUTO_forecasted_value AUTO_upper_95percentCL
1231 -649440 0 649440
1232 -649440 0 649440
1233 -649440 0 649440
1234 -649440 0 649440
1235 -649440 0 649440

Model equation and details:

Coefficients: 109794753100.511
sigma^2 estimated as: -17379.7497218715
log likelihood: 34761.4994437431
AIC: 34761.502701072
AICc: 34766.6142131914
BIC: 109794753100.511

Errors of the Automatic ARIMA model:

mean error (ME) 8481.52165393133
mean absolute error (MAE) 8598.17812314506
mean squared error (MSE) 154880315.96971
mean percentage error (MPE) 33.8198933472171
mean absolute percentage error (MAPE) 34.9279914586984

The next best forecasting model is:

Weighted Average Model

The following model is the Weighted Average model. Forecasted values and 95 percent confidence intervals of the next five observations are:

  WA_lower_95percentCL WA_forecasted_value WA_upper_95percentCL
1 -256797 8385 276355
2 -256826 8412 276561
3 -256853 8440 276768
4 -256879 8468 276975
5 -256905 8496 277183

Model equation:

WA_PRED = 0.42 * MA_PRED + 0.18 * REG_PRED + 0.4 * AUTO_PRED

where:

WA_PRED = predictions of the WA model

MA_PRED = predictions made by the ARIMA model

REG_PRED = predictions made by the Regression model

AUTO_PRED = predictions made by the Automatic ARIMA model

Errors of the WA model:

mean error (ME) 9709.26811209572
mean absolute error (MAE) 9709.26811209572
mean squared error (MSE) 177192572.762526
mean percentage error (MPE) 41.1714489811069
mean absolute percentage error (MAPE) 41.1714489811069

The next best forecasting model is:

Regression Model

The fitted regression model uses the observation number as the predictor variale. Forecasted values and 95 percent confidence intervals of the next five observations are:

  REG_lower_95percentCL REG_forecasted_value REG_upper_95percentCL
1 -211 4418 9048
2 -207 4423 9052
3 -202 4427 9057
4 -198 4432 9062
5 -193 4437 9066

Regression model:

REG_PRED = -1231 + 4.6 * t + e , where e ~ N ( 0 , 2356 )

where t is the observation number

Errors of the regression model:

mean error (ME) 15704.0561900534
mean absolute error (MAE) 15704.0561900534
mean squared error (MSE) 329555557.537419
mean percentage error (MPE) 76.8499542944693
mean absolute percentage error (MAPE) 76.8499542944693


Generated on: Tue Dec 12 14:51:13 2017 - R2HTML