During the pandemic, the stock prices almost doubled, but their trends have recently declined. One of the reasons for that might be the interest rates. To examine this, we will take a consideration ARK Innovation ETF (ARKK), which is a long-term growth capital by investing mostly in tech companies.
First, we will create our datasets. The interest rates we are going to use are long-term interest rates that induced investment, so which is related to economic growth.
library(tidyverse) library(tidyquant) library(sysfonts) library(showtext) library(gghighlight) library(tidymodels) library(timetk) library(modeltime) library(tsibble) library(lubridate) library(fable) library(ggtext) library(scales) #Building monthly dataset from daily prices arkk_monthly <- tq_get("ARKK") %>% mutate(month = floor_date(date, "month"), close = round(close, 2)) %>% group_by(month) %>% slice_max(date) %>% select(date, price = close, volume) #US long-term interest rates interest_df <- read_csv("https://raw.githubusercontent.com/mesdi/blog/main/interest.csv") %>% #converting string to date format mutate(date = parse_date(date, "%Y-%m")) #Combining the two datasets df <- arkk_monthly %>% left_join(interest_df, by = c("month"="date")) %>% #converts date to the given string format mutate(month = format(month, "%Y %b")) %>% #converts string to the yearmonth object mutate(month = yearmonth(month)) %>% ungroup() %>% select(-country) %>% na.omit()
Now, we will take a look at how the stock prices of ARKK and long-term interest rates have gone along together.
#Comparing stock prices and interest rates #adding google font font_add_google(name = "Space Mono", family = "Mono") showtext_auto() df %>% ggplot(aes(date))+ geom_bar(aes(y=price), stat = "identity", fill = "#69b3a2", color= NA, alpha = .4)+ geom_line(aes(y = price), color= "#69b3a2", size =2)+ geom_line(aes(y = interest*10), size =2, color = "#fcba03") + #highlights the area after 2019 gghighlight(year(date) >= 2019)+ scale_y_continuous( #Main axis labels = scales::label_dollar(), name = "Stock Price (ARKK)", #Add a second axis sec.axis = sec_axis(~./10, labels = scales::label_number(suffix = "%"), name="Interest Rate (FED)") ) + xlab("")+ theme_bw(base_family = "Mono") + theme( text = element_text(size = 20), axis.title.y = element_text(color = "#69b3a2"), axis.title.y.right = element_text(color = "#fcba03"), axis.text.y = element_text(color = "#69b3a2"), axis.text.y.right = element_text(color = "#fcba03") )
When we look at it, especially from 2019, we can clearly see the reverse relation between stock prices and interest rates.
Based on the above inference, we will model stock prices with interest rates. To do that, we will use boosted ARIMA regression model.
#Building train and test set df_split <- time_series_split(data = df, assess = "2 years", cumulative = TRUE) df_train <- training(df_split) df_test <- testing(df_split) #Modeling #Preprocessing df_rec <- recipe(price ~ interest + date, df_train) %>% step_fourier(date, period = 12, K = 6) #Model specification df_spec <- arima_boost( # XGBoost Args tree_depth = 6, learn_rate = 0.1) %>% set_engine(engine = "auto_arima_xgboost") #Worlflow and fitting workflow_df <- workflow() %>% add_recipe(df_rec) %>% add_model(df_spec) set.seed(12345) workflow_df_fit <- workflow_df %>% fit(data = df_train) #Model and calibration table model_table <- modeltime_table(workflow_df_fit) df_calibration <- model_table %>% modeltime_calibrate(df_test) #Accuracy df_calibration %>% modeltime_accuracy() %>% select(rsq) # A tibble: 1 x 1 # rsq # <dbl> #1 0.913
The high accuracy rate encourages us to proceed with that model. Now, we will forecast stock prices for the next 12 months. But first, we must build a dataset consisting of future values of predictors. We will use the automated stepwise ARIMA model for the interest rate variable.
#Future dataset for the next 12 months date <- df %>% as_tsibble(index= month) %>% new_data(12) %>% mutate(month = as.Date(month), date = ceiling_date(month, "month")-1) %>% as_tibble() %>% select(date) interest <- df %>% as_tsibble(index = month) %>% model(ARIMA(interest)) %>% forecast(h = 12) %>% as_tibble() %>% select(interest = .mean) df_future <- date %>% bind_cols(interest)
Finally, we refit the model on the whole dataset and draw the forecasting plot.
#Forecasting the next 12 months df_calibration %>% modeltime_refit(df) %>% modeltime_forecast(new_data = df_future, actual_data = df) %>% plot_modeltime_forecast(.interactive = FALSE, .legend_show = FALSE, .conf_interval_show = FALSE, .line_size = 1, .title = "Forecast Plot of ARK Innovation ETF Prices for the <span style = 'color:red;'>next 12 months</span>")+ scale_y_continuous(labels = scales::label_dollar())+ theme(text = element_text(size = 20, family = "Mono"), plot.title = ggtext::element_markdown(hjust = 0.5))
It looks like the prices will remain far below $50 in the coming year.
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