Séries Temporais com R: exemplo de Bitcoin com Facebook Prophet

Abstract

This is an undergrad student level instruction for class use.

Licença

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

License: CC BY-SA 4.0

Citação

Sugestão de citação: FIGUEIREDO, Adriano Marcos Rodrigues. Séries Temporais com R: exemplo de Bitcoin com Facebook Prophet. Campo Grande-MS,Brasil: RStudio/Rpubs, 2021. Disponível em http://rpubs.com/amrofi/prophet_bitcoin.

1 Introdução

Neste exemplo, utilizarei a rotina de Eloriaga (2020) para demonstrar o uso do pacote prophet em linguagem R. Esta rotina de estimação funciona bem para dados diários e neste caso é aplicado para um exemplo de preço de bitcoin, originado de Eloriaga (2020).

Para facilitar a reprodução do código, coloco os dados embedded, mas aqueles que desejarem, acessem o video de Eloriaga (2020) e peguem os dados no endereço formecido na descrição do video.

2 Pacotes utilizados

Para este exemplo, dois pacotes serão necessários e devem estar previamente instalados.

library(prophet)
library(tidyverse)

3 Carregando o Dataset

No presente post, coloquei dentro do arquivo Rmd. Ou seja, baixe o code e terás os dados dentro do arquivo baixado.

Podemos ver os dados, e temos que o prophet precisa de uma coluna \(ds\) para datas e outra \(y\) para os valores.

# 
head(bitcoin)

4 O Modelo Facebook Prophet

O ajuste será feito pela função prophet. Neste modo, o automático testará para sazonalidades diária, semanal, anual e feriados e ajustará aos dados. O default considera growth = “linear”, changepoints = NULL, n.changepoints = 25, changepoint.range = 0.8, yearly.seasonality = “auto”, weekly.seasonality = “auto”, daily.seasonality = “auto”, holidays = NULL, seasonality.mode = “additive” entre outras especificações.

Model1 <- prophet(bitcoin)
class(Model1)  # objeto do prophet

[1] "prophet" "list"   

4.1 Criar dataframe com mais 365 obs a frente (fora da amostra)

Future1 <- make_future_dataframe(Model1, periods = 365)
tail(Future1)

4.2 Previsao pelo Model1 para as datas de Future1

Forecast1 <- predict(Model1, Future1)
class(Forecast1)

[1] "data.frame"

4.3 Mostrar as últimas previsões do dataframe Forecast1

tail(Forecast1[c("ds", "yhat", "yhat_lower", "yhat_upper")])

4.4 Resíduos do Prophet

# adaptado de
# https://www.r-bloggers.com/2018/02/forecasting-pm2-5-with-forecast-and-prophet/
# Get the residuals modelo previsto Forecast1
Forecast1$ds <- as.Date(Forecast1$ds)
bitcoin$ds <- as.Date(bitcoin$ds)
fpred <- tsibble::as_tsibble(Forecast1, index = ds)
bit.tsb <- tsibble::as_tsibble(bitcoin, index = ds)
# Get the residuals

fpred <- bitcoin %>%
    left_join(fpred, by = "ds")
fpred$resid <- fpred$y - fpred$yhat
library(feasts)
fpred <- tsibble::as_tsibble(fpred, index = ds)
fpred %>%
    features(resid, unitroot_kpss)

# Plot the residuals
ggplot(fpred, aes(ds, resid)) + geom_line() + geom_smooth() + ggtitle("Resíduos Prophet",
    subtitle = paste0("RMSE: ", round(sqrt(mean(fpred$resid^2)), 2)))

4.5 Teste de raiz unitária na série

## Unit Root Test -------- KPSS Test H0:the data is stationary around a
## deterministic trend.
library(feasts)
bit.tsb %>%
    features(y, unitroot_kpss)

# rejeitou H0 e a série é não estacionária

4.6 Teste de raiz unitária nos resíduos

## Unit Root Test -------- KPSS Test H0:the data is stationary around a
## deterministic trend.
library(feasts)
fpred %>%
    features(resid, unitroot_kpss)

# não rejeitou H0 e a série de resíduos é estacionária, embora um p-valor baixo

4.7 Teste para efeitos ARCH no {feasts}: Engle(1982)

# ver
# https://rstudio-pubs-static.s3.amazonaws.com/346563_b404c507f20549f196f43c57d363595f.html

feasts::stat_arch_lm(bit.tsb$y)  # R^2 = 0.95 alta relacao entre lags e x^2 => tem ARCH

stat_arch_lm 
   0.9526924 

# se nao houvesse, o ajuste seria fraco e R2 seria baixo

4.8 Teste de Ljung-Box para autocorrelação residual

Existe alguma autocorrelação residual significativa diferente de zero (não rejeitou H0 de ausência de autocorrelação nos resíduos) desde o primeiro lag.

library(FitAR)  # pratico para plotar graficos de Q
# LBQPlot(res, lag.max = 30) res é a série que temos interesse de realizar os
# testes lag.max é o número de lags que se deseja imprimir o gráfico
LBQPlot(fpred$resid, 36)

4.9 Gráficos

4.9.1 Estimativas do Modelo

O prophet faz com recursos do dygraphs mostrando os pontos e a previsão.

dyplot.prophet(Model1, Forecast1)

4.9.2 Plot dos componentes tendência, sazonalidade semanal e anual pelo ggplot2

Plotará todos os componentes que estiverem no Model1 - podem ser sazonalidades, feriados, regressores externos - exógenos - aditivos ou multiplicativos.

prophet_plot_components(Model1, Forecast1)

5 Comparando com o fable.prophet

O fable.prophet é o pacote do O’Hara-Wild, Taylor e Letham (NA), que pretende dar o mesmo resultado que o prophet original, ou seja, apenas acomodando o arcabouço tsibble-fable.

Rodamos também o ETS e o ARIMA para acompanhar o código de Hyndman e Athanasopoulos (2020).

library(fable.prophet)
library(fpp3)
date <- as.Date(bitcoin$ds)
tbl1 <- tibble(date = date, value = bitcoin$y)
btc_tsbl <- as_tsibble(tbl1, index = date)

fit2 <- btc_tsbl %>%
    model(arima = ARIMA(value), ets = ETS(value), prophet = prophet(value)) %>%
    mutate(mixed = (ets + arima + prophet)/3)
fc2 <- fit2 %>%
    forecast(h = "1 year")
fc2 %>%
    autoplot(btc_tsbl)

5.1 Resíduos do fable.prophet

require(tidyverse)
require(fable.prophet)
resid.fabprophet <- fit2 %>%
    residuals()
residprophet <- resid.fabprophet %>%
    filter(.model == "prophet")
plot.ts(residprophet$.resid) + abline(h = 0, col = "blue")

integer(0)

6 Comparação das estimativas prophet x fable.prophet

knitr::kable(cbind(Forecast1[1826:2190, c("ds", "yhat")], fc2[731:1095, ".mean"]))

	ds	yhat	.mean
1826	2020-06-11	8900.484	8771.163
1827	2020-06-12	8941.338	8754.743
1828	2020-06-13	8981.451	8799.818
1829	2020-06-14	8990.072	8815.184
1830	2020-06-15	9033.357	8852.459
1831	2020-06-16	9052.059	8854.133
1832	2020-06-17	9080.692	8887.859
1833	2020-06-18	9092.834	8888.958
1834	2020-06-19	9132.611	8936.463
1835	2020-06-20	9169.477	8989.896
1836	2020-06-21	9172.888	8995.711
1837	2020-06-22	9209.237	9029.892
1838	2020-06-23	9219.543	9034.951
1839	2020-06-24	9238.601	9037.894
1840	2020-06-25	9240.277	9029.170
1841	2020-06-26	9268.982	9065.287
1842	2020-06-27	9294.449	9099.406
1843	2020-06-28	9286.395	9101.716
1844	2020-06-29	9311.450	9102.631
1845	2020-06-30	9310.844	9090.756
1846	2020-07-01	9319.547	9098.662
1847	2020-07-02	9311.569	9125.869
1848	2020-07-03	9331.427	9147.552
1849	2020-07-04	9348.922	9156.089
1850	2020-07-05	9333.805	9136.138
1851	2020-07-06	9352.706	9174.509
1852	2020-07-07	9346.826	9136.872
1853	2020-07-08	9351.079	9167.944
1854	2020-07-09	9339.397	9126.295
1855	2020-07-10	9356.204	9181.751
1856	2020-07-11	9371.199	9141.453
1857	2020-07-12	9354.022	9168.592
1858	2020-07-13	9371.196	9178.895
1859	2020-07-14	9363.817	9142.975
1860	2020-07-15	9366.705	9169.750
1861	2020-07-16	9353.713	9163.847
1862	2020-07-17	9369.201	9173.565
1863	2020-07-18	9382.820	9200.694
1864	2020-07-19	9364.188	9189.090
1865	2020-07-20	9379.818	9177.624
1866	2020-07-21	9370.822	9199.266
1867	2020-07-22	9372.051	9176.034
1868	2020-07-23	9357.402	9147.204
1869	2020-07-24	9371.295	9195.456
1870	2020-07-25	9383.449	9183.957
1871	2020-07-26	9363.552	9166.618
1872	2020-07-27	9378.191	9165.896
1873	2020-07-28	9368.546	9157.320
1874	2020-07-29	9369.530	9171.613
1875	2020-07-30	9355.090	9113.849
1876	2020-07-31	9369.680	9166.355
1877	2020-08-01	9383.037	9195.084
1878	2020-08-02	9364.846	9142.241
1879	2020-08-03	9381.672	9176.934
1880	2020-08-04	9374.650	9185.548
1881	2020-08-05	9378.628	9146.941
1882	2020-08-06	9367.468	9155.749
1883	2020-08-07	9385.523	9186.467
1884	2020-08-08	9402.411	9184.815
1885	2020-08-09	9387.692	9205.065
1886	2020-08-10	9407.795	9206.661
1887	2020-08-11	9403.718	9209.525
1888	2020-08-12	9410.172	9225.120
1889	2020-08-13	9400.892	9220.899
1890	2020-08-14	9420.112	9271.162
1891	2020-08-15	9437.348	9251.226
1892	2020-08-16	9422.074	9224.266
1893	2020-08-17	9440.660	9219.704
1894	2020-08-18	9434.065	9235.130
1895	2020-08-19	9436.989	9231.234
1896	2020-08-20	9423.181	9233.180
1897	2020-08-21	9436.918	9253.516
1898	2020-08-22	9447.782	9245.605
1899	2020-08-23	9425.337	9244.759
1900	2020-08-24	9436.063	9262.591
1901	2020-08-25	9421.045	9248.568
1902	2020-08-26	9415.121	9212.815
1903	2020-08-27	9392.188	9223.042
1904	2020-08-28	9396.667	9234.861
1905	2020-08-29	9398.288	9220.970
1906	2020-08-30	9366.751	9154.639
1907	2020-08-31	9368.659	9166.634
1908	2020-09-01	9345.204	9159.120
1909	2020-09-02	9331.312	9130.645
1910	2020-09-03	9300.937	9106.579
1911	2020-09-04	9298.540	9121.585
1912	2020-09-05	9293.857	9092.239
1913	2020-09-06	9256.570	9078.510
1914	2020-09-07	9253.238	9065.779
1915	2020-09-08	9224.985	9050.631
1916	2020-09-09	9206.648	9024.479
1917	2020-09-10	9172.078	9001.824
1918	2020-09-11	9165.619	8970.924
1919	2020-09-12	9156.888	8989.959
1920	2020-09-13	9115.447	8956.334
1921	2020-09-14	9107.743	8956.059
1922	2020-09-15	9074.801	8911.445
1923	2020-09-16	9051.379	8893.259
1924	2020-09-17	9011.279	8869.560
1925	2020-09-18	8998.821	8850.412
1926	2020-09-19	8983.636	8843.405
1927	2020-09-20	8935.339	8823.113
1928	2020-09-21	8920.469	8780.161
1929	2020-09-22	8880.183	8737.541
1930	2020-09-23	8849.411	8724.826
1931	2020-09-24	8802.162	8667.130
1932	2020-09-25	8782.998	8653.938
1933	2020-09-26	8761.817	8630.346
1934	2020-09-27	8708.520	8574.950
1935	2020-09-28	8689.943	8564.092
1936	2020-09-29	8647.545	8546.953
1937	2020-09-30	8616.549	8486.103
1938	2020-10-01	8571.237	8458.187
1939	2020-10-02	8556.418	8451.640
1940	2020-10-03	8542.196	8483.422
1941	2020-10-04	8498.632	8406.654
1942	2020-10-05	8492.661	8384.654
1943	2020-10-06	8465.779	8389.955
1944	2020-10-07	8453.171	8379.962
1945	2020-10-08	8429.006	8340.168
1946	2020-10-09	8437.904	8372.850
1947	2020-10-10	8449.696	8400.458
1948	2020-10-11	8434.096	8375.261
1949	2020-10-12	8457.619	8393.336
1950	2020-10-13	8461.272	8415.877
1951	2020-10-14	8479.695	8413.834
1952	2020-10-15	8486.466	8400.555
1953	2020-10-16	8525.574	8480.948
1954	2020-10-17	8566.207	8526.774
1955	2020-10-18	8577.424	8523.091
1956	2020-10-19	8625.101	8581.519
1957	2020-10-20	8649.632	8610.660
1958	2020-10-21	8685.092	8646.153
1959	2020-10-22	8704.551	8670.194
1960	2020-10-23	8751.574	8708.933
1961	2020-10-24	8795.011	8770.641
1962	2020-10-25	8803.687	8791.661
1963	2020-10-26	8843.361	8837.133
1964	2020-10-27	8854.429	8842.215
1965	2020-10-28	8871.094	8882.843
1966	2020-10-29	8866.683	8864.537
1967	2020-10-30	8885.142	8892.099
1968	2020-10-31	8895.826	8903.885
1969	2020-11-01	8868.179	8872.778
1970	2020-11-02	8868.679	8854.665
1971	2020-11-03	8838.530	8841.232
1972	2020-11-04	8812.817	8841.947
1973	2020-11-05	8765.801	8793.685
1974	2020-11-06	8742.393	8748.342
1975	2020-11-07	8712.925	8722.871
1976	2020-11-08	8647.804	8703.798
1977	2020-11-09	8614.436	8667.967
1978	2020-11-10	8554.896	8589.877
1979	2020-11-11	8505.055	8582.087
1980	2020-11-12	8439.864	8453.952
1981	2020-11-13	8404.804	8440.945
1982	2020-11-14	8370.638	8418.472
1983	2020-11-15	8308.063	8326.185
1984	2020-11-16	8284.612	8366.442
1985	2020-11-17	8242.327	8317.482
1986	2020-11-18	8216.883	8282.250
1987	2020-11-19	8182.870	8235.603
1988	2020-11-20	8185.250	8226.452
1989	2020-11-21	8194.126	8285.960
1990	2020-11-22	8179.398	8227.735
1991	2020-11-23	8207.689	8269.957
1992	2020-11-24	8220.032	8270.975
1993	2020-11-25	8251.024	8339.319
1994	2020-11-26	8274.124	8334.970
1995	2020-11-27	8333.146	8427.951
1996	2020-11-28	8397.044	8493.584
1997	2020-11-29	8434.599	8510.264
1998	2020-11-30	8511.375	8600.406
1999	2020-12-01	8567.428	8688.392
2000	2020-12-02	8636.475	8767.631
2001	2020-12-03	8691.228	8793.271
2002	2020-12-04	8774.889	8894.147
2003	2020-12-05	8855.960	8966.374
2004	2020-12-06	8902.936	9009.769
2005	2020-12-07	8981.262	9088.287
2006	2020-12-08	9031.050	9137.655
2007	2020-12-09	9086.249	9191.744
2008	2020-12-10	9119.960	9270.869
2009	2020-12-11	9175.931	9277.651
2010	2020-12-12	9223.346	9354.592
2011	2020-12-13	9231.503	9372.014
2012	2020-12-14	9266.751	9403.076
2013	2020-12-15	9270.181	9396.642
2014	2020-12-16	9276.771	9392.960
2015	2020-12-17	9260.677	9416.145
2016	2020-12-18	9266.701	9421.397
2017	2020-12-19	9265.053	9402.550
2018	2020-12-20	9226.002	9373.655
2019	2020-12-21	9216.794	9372.277
2020	2020-12-22	9179.318	9320.151
2021	2020-12-23	9149.233	9303.459
2022	2020-12-24	9101.245	9227.683
2023	2020-12-25	9080.564	9240.007
2024	2020-12-26	9057.654	9187.567
2025	2020-12-27	9002.888	9124.255
2026	2020-12-28	8983.462	9167.561
2027	2020-12-29	8941.064	9056.311
2028	2020-12-30	8911.018	9045.500
2029	2020-12-31	8867.564	9007.089
2030	2021-01-01	8855.339	9001.030
2031	2021-01-02	8844.143	8995.139
2032	2021-01-03	8803.614	8936.366
2033	2021-01-04	8800.166	8939.492
2034	2021-01-05	8774.686	8936.954
2035	2021-01-06	8761.695	8913.111
2036	2021-01-07	8734.661	8867.421
2037	2021-01-08	8737.494	8888.110
2038	2021-01-09	8739.343	8890.821
2039	2021-01-10	8709.285	8829.021
2040	2021-01-11	8713.279	8851.470
2041	2021-01-12	8691.879	8838.123
2042	2021-01-13	8679.404	8806.189
2043	2021-01-14	8649.257	8773.635
2044	2021-01-15	8645.420	8743.311
2045	2021-01-16	8637.250	8740.826
2046	2021-01-17	8594.161	8729.804
2047	2021-01-18	8582.571	8725.768
2048	2021-01-19	8543.596	8683.222
2049	2021-01-20	8512.202	8631.966
2050	2021-01-21	8462.513	8573.058
2051	2021-01-22	8439.275	8539.044
2052	2021-01-23	8412.633	8533.654
2053	2021-01-24	8352.785	8431.926
2054	2021-01-25	8326.909	8428.541
2055	2021-01-26	8276.830	8380.469
2056	2021-01-27	8238.152	8350.208
2057	2021-01-28	8185.540	8282.605
2058	2021-01-29	8164.170	8258.779
2059	2021-01-30	8144.490	8238.188
2060	2021-01-31	8096.863	8188.039
2061	2021-02-01	8088.478	8156.737
2062	2021-02-02	8061.026	8160.890
2063	2021-02-03	8049.822	8148.165
2064	2021-02-04	8029.094	8115.710
2065	2021-02-05	8043.444	8133.000
2066	2021-02-06	8062.618	8109.184
2067	2021-02-07	8056.168	8146.567
2068	2021-02-08	8090.383	8136.749
2069	2021-02-09	8105.982	8171.719
2070	2021-02-10	8137.266	8208.493
2071	2021-02-11	8157.429	8231.392
2072	2021-02-12	8210.049	8247.204
2073	2021-02-13	8263.882	8336.950
2074	2021-02-14	8287.548	8360.114
2075	2021-02-15	8346.494	8377.667
2076	2021-02-16	8380.702	8441.601
2077	2021-02-17	8423.865	8470.355
2078	2021-02-18	8448.716	8514.326
2079	2021-02-19	8498.529	8567.960
2080	2021-02-20	8541.924	8602.036
2081	2021-02-21	8547.563	8588.388
2082	2021-02-22	8581.103	8645.032
2083	2021-02-23	8582.911	8629.314
2084	2021-02-24	8587.228	8616.454
2085	2021-02-25	8567.485	8596.642
2086	2021-02-26	8567.790	8612.258
2087	2021-02-27	8557.713	8603.919
2088	2021-02-28	8506.960	8563.239
2089	2021-03-01	8482.303	8509.966
2090	2021-03-02	8425.264	8466.290
2091	2021-03-03	8371.260	8392.367
2092	2021-03-04	8294.884	8329.597
2093	2021-03-05	8241.367	8315.837
2094	2021-03-06	8181.342	8237.382
2095	2021-03-07	8085.484	8112.636
2096	2021-03-08	8021.428	8065.059
2097	2021-03-09	7931.428	7975.630
2098	2021-03-10	7851.488	7878.942
2099	2021-03-11	7756.630	7811.204
2100	2021-03-12	7692.353	7736.884
2101	2021-03-13	7629.383	7637.098
2102	2021-03-14	7538.326	7575.303
2103	2021-03-15	7486.582	7514.580
2104	2021-03-16	7416.015	7473.652
2105	2021-03-17	7362.095	7413.779
2106	2021-03-18	7299.188	7356.372
2107	2021-03-19	7272.024	7322.245
2108	2021-03-20	7250.477	7292.813
2109	2021-03-21	7204.234	7224.224
2110	2021-03-22	7199.735	7224.011
2111	2021-03-23	7177.873	7221.369
2112	2021-03-24	7173.153	7205.073
2113	2021-03-25	7159.006	7187.168
2114	2021-03-26	7179.285	7246.662
2115	2021-03-27	7203.062	7234.851
2116	2021-03-28	7199.312	7230.960
2117	2021-03-29	7233.873	7253.036
2118	2021-03-30	7247.154	7254.005
2119	2021-03-31	7273.306	7286.070
2120	2021-04-01	7285.536	7326.238
2121	2021-04-02	7327.607	7347.803
2122	2021-04-03	7368.630	7394.149
2123	2021-04-04	7377.746	7416.607
2124	2021-04-05	7421.072	7452.276
2125	2021-04-06	7439.397	7462.766
2126	2021-04-07	7467.339	7494.417
2127	2021-04-08	7478.645	7500.953
2128	2021-04-09	7517.667	7574.801
2129	2021-04-10	7554.136	7579.958
2130	2021-04-11	7557.826	7569.983
2131	2021-04-12	7595.478	7612.154
2132	2021-04-13	7608.478	7624.857
2133	2021-04-14	7631.994	7648.737
2134	2021-04-15	7640.263	7640.670
2135	2021-04-16	7678.051	7656.141
2136	2021-04-17	7715.414	7737.399
2137	2021-04-18	7722.357	7720.521
2138	2021-04-19	7765.748	7788.245
2139	2021-04-20	7786.998	7815.977
2140	2021-04-21	7821.194	7829.592
2141	2021-04-22	7842.393	7887.431
2142	2021-04-23	7895.086	7902.988
2143	2021-04-24	7948.972	7960.862
2144	2021-04-25	7973.625	7968.334
2145	2021-04-26	8035.424	8023.303
2146	2021-04-27	8075.248	8083.168
2147	2021-04-28	8127.624	8096.134
2148	2021-04-29	8166.040	8156.761
2149	2021-04-30	8234.428	8244.982
2150	2021-05-01	8301.950	8298.463
2151	2021-05-02	8337.685	8321.934
2152	2021-05-03	8407.575	8397.649
2153	2021-05-04	8452.127	8447.434
2154	2021-05-05	8505.581	8497.592
2155	2021-05-06	8541.226	8531.729
2156	2021-05-07	8602.887	8592.977
2157	2021-05-08	8659.722	8625.155
2158	2021-05-09	8680.906	8662.699
2159	2021-05-10	8732.569	8708.747
2160	2021-05-11	8755.507	8762.306
2161	2021-05-12	8784.328	8760.439
2162	2021-05-13	8792.768	8772.712
2163	2021-05-14	8825.164	8813.514
2164	2021-05-15	8851.236	8833.894
2165	2021-05-16	8840.756	8833.033
2166	2021-05-17	8860.478	8853.834
2167	2021-05-18	8851.820	8827.565
2168	2021-05-19	8850.009	8823.219
2169	2021-05-20	8829.369	8803.114
2170	2021-05-21	8834.787	8818.035
2171	2021-05-22	8836.481	8816.769
2172	2021-05-23	8804.654	8770.660
2173	2021-05-24	8806.417	8814.558
2174	2021-05-25	8783.464	8750.617
2175	2021-05-26	8771.209	8745.616
2176	2021-05-27	8744.071	8710.272
2177	2021-05-28	8746.944	8719.085
2178	2021-05-29	8749.962	8725.353
2179	2021-05-30	8723.158	8684.374
2180	2021-05-31	8733.394	8695.523
2181	2021-06-01	8722.045	8715.223
2182	2021-06-02	8724.144	8681.764
2183	2021-06-03	8713.681	8666.498
2184	2021-06-04	8735.079	8684.459
2185	2021-06-05	8757.976	8715.411
2186	2021-06-06	8751.903	8698.733
2187	2021-06-07	8783.213	8741.091
2188	2021-06-08	8792.789	8729.873
2189	2021-06-09	8815.195	8765.797
2190	2021-06-10	8823.990	8778.084

Existem pequenas diferenças que precisam ser investigadas (prometo fazer isso), pois provavelmente estão associadas aos defaults utilizados em cada pacote. Existe um aviso no manual que indica: Warning: The inputs controlling the seasonal period is specified is different than prophet::prophet(). Numeric inputs are treated as the number of observations in each seasonal period, not the number of days.

7 Fazendo uma janela de treino e com transformação Box-Cox

lambda = (forecast::BoxCox.lambda(btc_tsbl$value))
lambda

[1] -0.1026148

Vou deixar as estimações sem o lambda da transformação Box-Cox por enquanto.

8 Dividindo train x test

Como sugestão, ver HYndman e Athanasopoulos (2020, https://otexts.com/fpp3/prophet.html).

train <- btc_tsbl %>%
    filter_index(~"2019-06-11")  # 1825*.8 = 1460

A regra de divisão do treino (train) foi de 80-20.

9 Modelo

Vou rodar o modelo no treino e classificar pelo RMSE da acurácia. A parte de treino serão as 365 observações finais.

fit3 <- train %>%
    model(arima = ARIMA(value), ets = ETS(value), prophet = prophet(value)) %>%
    mutate(mixed = (ets + arima + prophet)/3)
fc3 <- fit3 %>%
    forecast(h = "2 years")
fc3 %>%
    autoplot(btc_tsbl, level = NULL) + labs(y = "Valor", title = "Previsão de Bitcoin")

É possível interpretar que com a definição do train em uma fase ascendente, ele capturou esta tendência um pouco exagerada. É possível refazer o treino para um momento diferente e comparar, mas deixaremos isso para o pesquisador. Segue a acurácia desse modelo com esse treino.

9.1 Acurácia

O leitor poderá verificar que o forecast com ETS nesse exemplo parece alterar muito a qualidade do modelo mixed, assim como a escolha do período de corte para o treino teve efeito importante sobre as estimativas. Deixo a cargo do usuário treinar com outros intervalos, que com certeza obterão melhores estimativas.
(ver https://robjhyndman.com/hyndsight/fable/)

# this will take some time to estimate
fc_accuracy <- accuracy(fc3, btc_tsbl, measures = list(point_accuracy_measures, interval_accuracy_measures,
    distribution_accuracy_measures))
# acurácia ordenada pelo RMSE
fc_accuracy %>%
    group_by(.model) %>%
    summarise(RMSE = mean(RMSE), MAE = mean(MAE), MASE = mean(MASE), Winkler = mean(winkler),
        CRPS = mean(CRPS)) %>%
    arrange(RMSE)

Referências

ELORIAGA, Justin Raymond S. (2020) Forecasting using Prophet in R. Youtube. Available at: https://youtu.be/4784Ait88G8

HYNDMAN, Rob. (2019). fpp3: Data for “Forecasting: Principles and Practice” (3rd Edition). R package. Disponível em: https://github.com/robjhyndman/fpp3-package, https://OTexts.org/fpp3/.

HYNDMAN, R.J.; ATHANASOPOULOS, G. (2020) Forecasting: principles and practice, 3rd edition, OTexts: Melbourne, Australia. Disponível em: https://otexts.com/fpp3/. Accessed on 02 Apr 2020.

O’HARA-WILD, Mitchell; TAYLOR, Sean; LETHAM, Ben (NA). fable.prophet: Prophet Modelling Interface for ‘fable’. R package version 0.1.0.9000. Available at: https://pkg.mitchelloharawild.com/fable.prophet/.

TAYLOR, Sean; LETHAM, Ben (2021). prophet: Automatic Forecasting Procedure. R package version 1.0. Available at: https://CRAN.R-project.org/package=prophet.

TAYLOR, Sean; LETHAM, Ben (2017). Forecasting at scale. PeerJ Preprints 5:e3190v2 https://doi.org/10.7287/peerj.preprints.3190v2