Update README.md

README.md

@@ -37,7 +37,6 @@ Cost of carry model; Vector error correction model; Engle-Grangle test; Johansen
 - CU.xlsx: contains the data of SHFE copper 
   - in four levels: cash price, future price, inventory, interest rate of government bonds.
   - in the historical period of 2009/12/31 - 2020/07/03
-  - 
 ## Project Research
 
 ## Project Introduction
@@ -75,13 +74,16 @@ $$ DP_t = a_0 + a_1 DF_{t|t-1} + e_t \tag{1} $$
 $$ DP_t = b_0 + b_1 (F_{t|t-1} - P_{t-1}) + e_t \tag{2} $$
 - Brenner and Kroner Model(1995):  
 $$ DP_t = g_0 + g_1 DF_{t|t-1} + g_2 Dr_{t|t-1} + g_3 DI_{t-1} + g_4 D\sigma_{t-1}+$$
-$$ g_5 D\rho(1)_{t-1} + g_6ECT_{t-2} + e_t \tag{3} $$
+$$ g_5 D\rho (1)_{t-1} + g_6ECT_{t-2} + e_t \tag{3} $$
 
 The error correction term, $ECT_{t-2}$ is the residual, $e_{t-1}$ from the regression:
-$$ P_{t-1} = h_0 + h_1 F_{t-1|t-2} + h_2 r_{t-1|t-2} + \newline h_3I_{t-2} +h_4 \sigma_{t-2} + h_5\rho(1)_{t-2} + e_{t-1} $$
+$$ P_{t-1} = h_0 + h_1 F_{t-1|t-2} + h_2 r_{t-1|t-2} + h_3I_{t-2} +h_4 \sigma_{t-2} + h_5\rho (1)_{t-2} + e_{t-1} $$
 
 - Vector Error Correction Model:
 $$ DX_t =  M_1 DX_{t-1} + S^{'}ECT_{t-2}^{*} + L + E_t \tag{4} $$
-$DX_t$ is the change in vector $X$, $M_1$ is the matrix of parameters, $S$ is the vector of speed of adjustment parameters, $L$ is a vector of constant terms and $E_t$ is the vector of residuals. $ECT^*_{t-2}$ are the residuals, $e_t$ from the following regression. 
-$$ P_{t-2} = j_0 + j_1 F_{t-1|t-2} + j_2 r_{t-1|t-2} + j_3I_{t-2} + j_4 \sigma_{t-2} + j_5\rho(1)_{t-2} + e_{t-1}$$
+
+$DX_t$ is the change in vector $X$, $M_1$ is the matrix of parameters, $S$ is the vector of speed of adjustment parameters, $L$ is a vector of constant terms and $E_t$ is the vector of residuals.$ECT^{*}_{t-2}$ are the residuals, $e_t$ from the following regression. 
+
+$$ P_{t-2} = j_0 + j_1 F_{t-1|t-2} + j_2 r_{t-1|t-2} + j_3I_{t-2} + j_4 \sigma_{t-2} + j_5\rho(1)_{t-2} + e_{t-1} $$
+
 with $i_i$ and $j_i$ as estimated parameters.