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 29.49% per annum.
- TJX price at the close of January 14, 2026 was $155.13 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 59.00% per annum.
- TJX price at the close of January 14, 2026 was inside the secondary price channel.
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 4, 2022
End date: January 14, 2026
a = 3.7436
b = 0.0007
s = 0.0494
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 29.49%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0494) – 1
= 21.86%
March 4, 2022 calculations
Top border of price channel:
Exp(Y285)
= Exp(a + b × X285 + 2 × s)
= Exp(a + b × 413 + 2 × s)
= Exp(3.7436 + 0.0007 × 413 + 2 × 0.0494)
= Exp(4.1349)
= $62.48
Bottom border of price channel:
Exp(Y285)
= Exp(a + b × X285 – 2 × s)
= Exp(a + b × 413 – 2 × s)
= Exp(3.7436 + 0.0007 × 413 – 2 × 0.0494)
= Exp(3.9372)
= $51.27
January 14, 2026 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(3.7436 + 0.0007 × 1,825 + 2 × 0.0494)
= Exp(5.1348)
= $169.83
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(3.7436 + 0.0007 × 1,825 – 2 × 0.0494)
= Exp(4.9370)
= $139.36
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 29.49% per annum.
- TJX price at the close of January 14, 2026 was $155.13 and was inside the primary price channel.
Secondary Trend
Start date: June 11, 2025
End date: January 14, 2026
a = 2.7539
b = 0.0013
s = 0.0196
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0013) – 1
= 59.00%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0196) – 1
= 8.17%
June 11, 2025 calculations
Top border of price channel:
Exp(Y1,105)
= Exp(a + b × X1,105 + 2 × s)
= Exp(a + b × 1,608 + 2 × s)
= Exp(2.7539 + 0.0013 × 1,608 + 2 × 0.0196)
= Exp(4.8361)
= $125.98
Bottom border of price channel:
Exp(Y1,105)
= Exp(a + b × X1,105 – 2 × s)
= Exp(a + b × 1,608 – 2 × s)
= Exp(2.7539 + 0.0013 × 1,608 – 2 × 0.0196)
= Exp(4.7576)
= $116.47
January 14, 2026 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(2.7539 + 0.0013 × 1,825 + 2 × 0.0196)
= Exp(5.1118)
= $165.97
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(2.7539 + 0.0013 × 1,825 – 2 × 0.0196)
= Exp(5.0333)
= $153.44
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 59.00% per annum.
- TJX price at the close of January 14, 2026 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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