library(dplyr)
library(tseries)
library(rlist)
library(knitr)
library(urca)
library(ggplot2)
library(tidyr)
library(magrittr)
library(corrr)

重製 (Ciaian, Rajcaniova, and Kancs 2014)

比特幣貨幣供給：

\[M^S = P^B B \]

貨幣需求

\[M^D = \frac{PY}{V}\]

在貨幣供給與貨幣需求交叉時，隱含下式成立

\[ P^B = \frac{PY}{VB}\]

取 log 後

\[ p^B_t = \beta_0 +\beta_1 p_t +\beta_2 y_t +\beta_3 v_t +\beta_4 b_t + \epsilon_t\]

all_data <- readRDS("data/all_data.rda")
all_data <- all_data %>% filter(Date<"2014-12-31")
all_data %>% glimpse()
## Observations: 1,264
## Variables: 12
## $ Date        <date> 2014-12-30, 2014-12-29, 2014-12-24, 2014-12-23, 2...
## $ mkpru       <dbl> 181005, 159314, 174711, 210726, 195624, 160502, 22...
## $ totbc       <dbl> 13666700, 13663050, 13642825, 13639050, 13635000, ...
## $ ntran       <dbl> 85247, 79812, 89515, 99770, 89437, 92052, 103161, ...
## $ naddu       <dbl> 181005, 159314, 174711, 210726, 195624, 160502, 22...
## $ bcdde       <dbl> 16810168, 3589855, 27154619, 3800448, 5495943, 449...
## $ exrate      <dbl> 1.2160, 1.2197, 1.2219, 1.2213, 1.2259, 1.2279, 1....
## $ wiki_views  <dbl> 6162, 9927, 3904, 4752, 5168, 4905, 5563, 6328, 69...
## $ new_members <dbl> 301, 297, 231, 271, 285, 272, 376, 307, 286, 285, ...
## $ new_posts   <dbl> 9460, 9538, 8451, 9903, 10031, 9884, 10509, 11248,...
## $ oil_price   <dbl> 55.60, 57.86, 58.67, 59.07, 58.31, 58.87, 58.81, 5...
## $ dj          <dbl> 17983.07, 18038.23, 18030.21, 18024.17, 17959.44, ...
all_data %>%
  gather(key = "column", value="value", -Date, factor_key = T) %>%
  ggplot(aes(x= Date, y= value)) +
  geom_line() +
  facet_wrap(~column, scales = "free_y", ncol = 3)

pretty_cor <- . %>% correlate() %>% shave %>% fashion() %>% kable(align = "r")
all_data %>% select(-Date, -mkpru) %>% pretty_cor
rowname totbc ntran naddu bcdde exrate wiki_views new_members new_posts oil_price dj
totbc
ntran .90
naddu .82 .93
bcdde .29 .30 .27
exrate -.24 -.24 -.13 .00
wiki_views .44 .50 .48 .43 .08
new_members .43 .47 .52 .49 .12 .57
new_posts .77 .83 .91 .26 .04 .56 .61
oil_price .46 .15 .05 .15 .25 .22 .18 .20
dj .93 .94 .92 .28 -.14 .46 .48 .87 .29

做 ADF 與 PP

論文上面表示所有序列都不平穩

Both tests show that all the time series are non-stationary in levels but stationary in first differences (results of the tests are available upon request from authors).

apply_stationary_test <- function(df, test) df %>%
  select_if(is.numeric) %>%
  lapply(test) %>%
  list.rbind() %>%
  as.data.frame() %>%
  .[,1:5]

all_data %>% apply_stationary_test(adf.test) %>% kable
statistic parameter alternative p.value method
mkpru -2.029021 10 stationary 0.5660283 Augmented Dickey-Fuller Test
totbc -1.461064 10 stationary 0.8064528 Augmented Dickey-Fuller Test
ntran -2.70011 10 stationary 0.2819463 Augmented Dickey-Fuller Test
naddu -2.029021 10 stationary 0.5660283 Augmented Dickey-Fuller Test
bcdde -8.684171 10 stationary 0.01 Augmented Dickey-Fuller Test
exrate -2.113085 10 stationary 0.5304425 Augmented Dickey-Fuller Test
wiki_views -4.528032 10 stationary 0.01 Augmented Dickey-Fuller Test
new_members -4.897156 10 stationary 0.01 Augmented Dickey-Fuller Test
new_posts -1.798901 10 stationary 0.6634413 Augmented Dickey-Fuller Test
oil_price -3.643006 10 stationary 0.02854341 Augmented Dickey-Fuller Test
dj -3.192426 10 stationary 0.08922365 Augmented Dickey-Fuller Test 
all_data %>% apply_stationary_test(pp.test) %>% kable
statistic parameter alternative p.value method
mkpru -27.9347 7 stationary 0.01354644 Phillips-Perron Unit Root Test
totbc -0.5681851 7 stationary 0.99 Phillips-Perron Unit Root Test
ntran -92.09774 7 stationary 0.01 Phillips-Perron Unit Root Test
naddu -27.9347 7 stationary 0.01354644 Phillips-Perron Unit Root Test
bcdde -924.5475 7 stationary 0.01 Phillips-Perron Unit Root Test
exrate -10.26176 7 stationary 0.5373211 Phillips-Perron Unit Root Test
wiki_views -134.5997 7 stationary 0.01 Phillips-Perron Unit Root Test
new_members -869.9306 7 stationary 0.01 Phillips-Perron Unit Root Test
new_posts -13.40014 7 stationary 0.3622546 Phillips-Perron Unit Root Test
oil_price -14.12571 7 stationary 0.3217809 Phillips-Perron Unit Root Test
dj -25.01554 7 stationary 0.0242203 Phillips-Perron Unit Root Test 
first_diff_df <- all_data %>% select(-Date) %>% lapply(diff) %>% bind_cols()
first_diff_df %>% apply_stationary_test(adf.test) %>% kable
statistic parameter alternative p.value method
mkpru -12.80136 10 stationary 0.01 Augmented Dickey-Fuller Test
totbc -6.467923 10 stationary 0.01 Augmented Dickey-Fuller Test
ntran -13.62754 10 stationary 0.01 Augmented Dickey-Fuller Test
naddu -12.80136 10 stationary 0.01 Augmented Dickey-Fuller Test
bcdde -17.23255 10 stationary 0.01 Augmented Dickey-Fuller Test
exrate -9.786337 10 stationary 0.01 Augmented Dickey-Fuller Test
wiki_views -14.50567 10 stationary 0.01 Augmented Dickey-Fuller Test
new_members -15.66745 10 stationary 0.01 Augmented Dickey-Fuller Test
new_posts -11.15824 10 stationary 0.01 Augmented Dickey-Fuller Test
oil_price -10.48832 10 stationary 0.01 Augmented Dickey-Fuller Test
dj -10.71333 10 stationary 0.01 Augmented Dickey-Fuller Test 
first_diff_df %>% apply_stationary_test(pp.test) %>% kable
statistic parameter alternative p.value method
mkpru -1305.826 7 stationary 0.01 Phillips-Perron Unit Root Test
totbc -1466.206 7 stationary 0.01 Phillips-Perron Unit Root Test
ntran -1243.034 7 stationary 0.01 Phillips-Perron Unit Root Test
naddu -1305.826 7 stationary 0.01 Phillips-Perron Unit Root Test
bcdde -1284.579 7 stationary 0.01 Phillips-Perron Unit Root Test
exrate -1304.655 7 stationary 0.01 Phillips-Perron Unit Root Test
wiki_views -1001.555 7 stationary 0.01 Phillips-Perron Unit Root Test
new_members -1461.68 7 stationary 0.01 Phillips-Perron Unit Root Test
new_posts -1179.383 7 stationary 0.01 Phillips-Perron Unit Root Test
oil_price -1260.413 7 stationary 0.01 Phillips-Perron Unit Root Test
dj -1302.082 7 stationary 0.01 Phillips-Perron Unit Root Test

Co-integration Test

# all_data %>% select(-Date) %>% ca.jo(type="eigen", K=2, ecdet="none", spec="longrun")

Ciaian, Pavel, Miroslava Rajcaniova, and D’Artis Kancs. 2014. “The Economics of BitCoin Price Formation,” May. http://arxiv.org/abs/1405.4498.