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 32.03% per annum.
- TJX price at the close of January 17, 2025 was $121.85 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 33.42% per annum.
- TJX price at the close of January 17, 2025 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: January 17, 2025
a = 3.4390
b = 0.0008
s = 0.0483
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0008) – 1
= 32.03%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0483) – 1
= 21.32%
March 7, 2022 calculations
Top border of price channel:
Exp(Y536)
= Exp(a + b × X536 + 2 × s)
= Exp(a + b × 776 + 2 × s)
= Exp(3.4390 + 0.0008 × 776 + 2 × 0.0483)
= Exp(4.1264)
= $61.96
Bottom border of price channel:
Exp(Y536)
= Exp(a + b × X536 – 2 × s)
= Exp(a + b × 776 – 2 × s)
= Exp(3.4390 + 0.0008 × 776 – 2 × 0.0483)
= Exp(3.9332)
= $51.07
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(3.4390 + 0.0008 × 1,823 + 2 × 0.0483)
= Exp(4.9235)
= $137.49
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(3.4390 + 0.0008 × 1,823 – 2 × 0.0483)
= Exp(4.7303)
= $113.33
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 32.03% per annum.
- TJX price at the close of January 17, 2025 was $121.85 and was inside the primary price channel.
Secondary Trend
Start date: November 26, 2024
End date: January 17, 2025
a = 6.8163
b = -0.0011
s = 0.0105
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0011) – 1
= -33.42%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0105) – 1
= 4.30%
November 26, 2024 calculations
Top border of price channel:
Exp(Y1,222)
= Exp(a + b × X1,222 + 2 × s)
= Exp(a + b × 1,771 + 2 × s)
= Exp(6.8163 + -0.0011 × 1,771 + 2 × 0.0105)
= Exp(4.8635)
= $129.47
Bottom border of price channel:
Exp(Y1,222)
= Exp(a + b × X1,222 – 2 × s)
= Exp(a + b × 1,771 – 2 × s)
= Exp(6.8163 + -0.0011 × 1,771 – 2 × 0.0105)
= Exp(4.8214)
= $124.14
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(6.8163 + -0.0011 × 1,823 + 2 × 0.0105)
= Exp(4.8055)
= $122.18
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(6.8163 + -0.0011 × 1,823 – 2 × 0.0105)
= Exp(4.7634)
= $117.15
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 33.42% per annum.
- TJX price at the close of January 17, 2025 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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