Analyzing the Interdependence between Copper Base Metal and Copper Scrap over the past 10 years (2010-20) that helps to Predict the #1 Copper Scrap based on COMEX EOD (End of Day) prices of primary Copper prices.
Author: C.G.Nadar
Editor: Jenisha
Research: Rakesh, C.G.Nadar
Commodity: Copper Base Metal, #1 Copper Scrap
Data: COMEX Copper EOD, 2010 -2020, RIM Copper Scrap Prices 2010-2020
Technology: Tensorflow, Keras, Scipy, Numpy
Research Methods:
- Augmented Dickey-Fuller (ADF),
- Kwiatkowski-Phillips-Schmidt-Shin (KPSS)
- Johansen method
- Granger’s Causality
- Bivariate Cointegration
Predictions: KERAS, VAR
Introduction
This aim of this research is to study how the Copper (base metal) prices are linked to the #1 Scrap copper prices over a time period. The tests are run with a long term time series (10 years) price linkage and causalities among the copper futures, primary and #1 copper scrap markets.
Copper scrap is an essential domestic resource for countries that depend on imports of copper ore especially from a handful of countries. The availability and the sustainability of copper ore may become scarce in the coming years which make recycling of copper a quintessential factor. With green energy initiatives around the Globe with Electric Vehicles, Electricity generation, Transmission infrastructure, Energy storage (Batteries) and consumption all require copper. This makes the correlation of prices of primary copper metal and copper scrap stronger compared to the prior 2000 scenario. We will analyze the interdependence between copper base metal and copper scrap over the past 10 years (2010-20) and help predict the #1 Copper scrap based on COMEX EOD (End of Day) prices of primary Copper prices. Analyzing the correlation of copper primary and copper scrap will be helpful in predicting the copper scrap prices from primary market price. This will provide valuable insights to scrap copper producers, traders, exporters, importers and copper recycling companies.
Data and Research for Correlation between Primary Copper & Copper Scrap
This copper price research the primary copper price and #1 scrap copper price. The time periods used for this research are 2010-2020. The COMEX copper EOD price is used to represent primary copper price. Average weekly, monthly quarterly and yearly copper prices are derived from the COMEX copper data. COMEX copper prices are in USD/lbs. These prices are converted to USD/Ton to simplify the export import prices of copper scrap which is calculated USD/Ton.
The #1 copper scrap prices are obtained from recycleinme.com for the same period (2010-2020). This price is also averaged for weekly, monthly quarterly and yearly averages to compare with primary copper prices from COMEX.
Data Preprocessing
The dates which are not matching in base metal and copper scrap prices are removed and so are the NULL values.
df.isnull().sum()
date 0
close price 0
ScrapPrice 0
dtype: int64
We have removed all the mismatching dates and null values from the data for an accurate analysis. Let us plot this data.
Graphical Representation of Primary Copper Price VS #1 Copper Scrap
The patterns are almost identical for both primary and scrap copper. This indicates the linkage of scrap copper prices with primary copper. To confirm this below tests were performed for accurate analysis and establish the correlation between the primary and scrap copper prices.
Augmented Dickey–Fuller test
The Augmented Dickey-Fuller test is a unit root test to check stationarity for a time series. The Augmented Dickey-Fuller test can be used with serial correlation.
We use the ADF test to check if the primary and scrap copper time series data are stationary or not. Since the initial test P-Value = 0.3235 indicates weak evidence to reject the Null Hypothesis we assume that the series is Non stationary. So we apply the second difference of first differenced dataset to check if the series is stationary.
The ADF test results for primary and copper scrap time series rejects Null hypothesis and the series is stationary.
KPSS test to check if the copper price time series is stationary
KPSS(Kwiatkowski-Phillips-Schmidt-Shin) test is a statistical test to check for stationarity of a time series similar to ADF test. This unit root test is conducted to check for Null Hypothesis.
KPSS test was run on the copper price time series with 80% training data and 20% test data. The following results are derived from the first run.
- KPSS Statistic: 2.3199671956105843
- p-value: 0.01
- num lags: 27
- Critial Values:
- 10% : 0.347
- 5% : 0.463
- 2.5% : 0.574
- 1% : 0.739
Result: The series is not stationary
The test indicates the p-value is significant (with p_value < 0.05) and hence rejects the null hypothesis (series is stationary) and derive that the series is NOT stationary.
The copper time series dataset is not stationary. To try and make the dataset stationary we take the first difference of the dataset.
- KPSS Statistic: 0.5718380913859195
- p-value: 0.02548691635452264
- num lags: 27
- Critial Values:
- 10% : 0.347
- 5% : 0.463
- 2.5% : 0.574
- 1% : 0.739
Result: The series is not stationary for the first difference
Since the first difference too is not stationary for the copper price time series, we take the second difference of the time series and test for stationarity.
- KPSS Statistic: 0.00730356533420672
- p-value: 0.1
- num lags: 27
- Critial Values:
- 10% : 0.347
- 5% : 0.463
- 2.5% : 0.574
- 1% : 0.739
Result: The series is stationary for the second difference.
Granger’s Causality Test
The Granger causality test is a statistical hypothesis test for determining whether one time series is useful for forecasting another. If probability value is less than any alpha level, then the hypothesis would be rejected at that level. We use the Grangers causality test to determine the correlation between the base copper price with #1 copper scrap price for the given time series.
Source: wikepedia.org
When time series X Granger-causes time series Y, the patterns in X are approximately repeated in Y after some time lag (two examples are indicated with arrows). Thus, past values of X can be used for the prediction of future values of Y.
Grangers Causality Test Results
The P-Value of 0.0048 at (row 1, column 2) represents the p-value of the Grangers Causality test for Copper Scrap close price_x causing Base metal close price_y, which is way less that the significance level of 0.05 which confirms the linkage of #1 Scrap prices with the primary copper prices.
#1 Copper Scrap Predictions from Primary Copper prices using VAR model
Vector autoregression (VAR) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type of stochastic process model. VAR models generalize the single-variable (univariate) autoregressive model by allowing for multivariate time series.
We use the VAR model to predict scrap copper prices from primary copper price. We first select the minimum AIC or BIC value for the lag order. We get a minimum lag order from the AIC value. So we use lag order as 10. If the predicted value is over fitting or not relevant, then we check with minimum BIC value.
VAR Model Summary
Summary of Regression Results
Model: | VAR |
Method: | OLS |
Date: | Thu, 27, May, 2021 |
Time: | 10:02:06 |
No. of Equations: | 2.00000 | BIC: -17.5671 |
Nobs: | 1781.00 | HQIC: -17.6487 |
Log likelihood: | 10746.5 | FPE: 2.06307e-08 |
AIC: | -17.6965 | Det(Omega_mle): 2.01526e-08 |
The copper scrap forecasts are generated but it is on the scale of the training data used by the model (0-1). So, to bring it back up to its original scale, we need to de-difference it This process can be reversed by adding the observation at the prior time step to the difference value. inverted(ts) = differenced(ts) + observation(ts-1)
Predicted value for #1 Copper Scrap price from Base metal copper price
Copper | #1 Scrap Actual | #1 Scrap Predicted |
4.0135 | 3.53 | 3.515086 |
4.0355 | 3.49 | 3.502356 |
4.1440 | 3.50 | 3.491081 |
4.1440 | 3.51 | 3.479035 |
4.1600 | 3.53 | 3.466823 |
4.1130 | 3.49 | 3.455570 |
4.1080 | 3.49 | 3.446691 |
4.0715 | 3.51 | 3.439250 |
Conclusion: Our VAR model predicts the copper scrap prices with an accuracy of over 96%. RIM research team with the help of our AI wing continues research on copper scrap prices and we will update it here as and when we get the sustainable results. Subscribe for Current Copper Scrap prices and Base Metal Prices.