Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 31.92% per annum.
- TJX price at the close of November 19, 2024 was $119.56 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 7.91% per annum.
- TJX price at the close of November 19, 2024 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of TJX price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: March 7, 2022
End date: November 19, 2024
a = 3.3945
b = 0.0008
s = 0.0491
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0008) – 1
= 31.92%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0491) – 1
= 21.71%
March 7, 2022 calculations
Top border of price channel:
Exp(Y576)
= Exp(a + b × X576 + 2 × s)
= Exp(a + b × 838 + 2 × s)
= Exp(3.3945 + 0.0008 × 838 + 2 × 0.0491)
= Exp(4.1288)
= $62.10
Bottom border of price channel:
Exp(Y576)
= Exp(a + b × X576 – 2 × s)
= Exp(a + b × 838 – 2 × s)
= Exp(3.3945 + 0.0008 × 838 – 2 × 0.0491)
= Exp(3.9323)
= $51.03
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.3945 + 0.0008 × 1,826 + 2 × 0.0491)
= Exp(4.8787)
= $131.46
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.3945 + 0.0008 × 1,826 – 2 × 0.0491)
= Exp(4.6822)
= $108.01
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 31.92% per annum.
- TJX price at the close of November 19, 2024 was $119.56 and was inside the primary price channel.
Secondary Trend
Start date: August 21, 2024
End date: November 19, 2024
a = 5.1596
b = -0.0002
s = 0.0198
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -7.91%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0198) – 1
= 8.23%
August 21, 2024 calculations
Top border of price channel:
Exp(Y1,194)
= Exp(a + b × X1,194 + 2 × s)
= Exp(a + b × 1,736 + 2 × s)
= Exp(5.1596 + -0.0002 × 1,736 + 2 × 0.0198)
= Exp(4.8074)
= $122.41
Bottom border of price channel:
Exp(Y1,194)
= Exp(a + b × X1,194 – 2 × s)
= Exp(a + b × 1,736 – 2 × s)
= Exp(5.1596 + -0.0002 × 1,736 – 2 × 0.0198)
= Exp(4.7283)
= $113.10
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(5.1596 + -0.0002 × 1,826 + 2 × 0.0198)
= Exp(4.7871)
= $119.95
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.1596 + -0.0002 × 1,826 – 2 × 0.0198)
= Exp(4.7080)
= $110.83
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 7.91% per annum.
- TJX price at the close of November 19, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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