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 29.35% per annum.
- TJX price at the close of April 15, 2026 was $160.23 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 24.48% per annum.
- TJX price at the close of April 15, 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: April 15, 2026
a = 3.8078
b = 0.0007
s = 0.0482
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 29.35%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0482) – 1
= 21.28%
March 4, 2022 calculations
Top border of price channel:
Exp(Y223)
= Exp(a + b × X223 + 2 × s)
= Exp(a + b × 322 + 2 × s)
= Exp(3.8078 + 0.0007 × 322 + 2 × 0.0482)
= Exp(4.1313)
= $62.26
Bottom border of price channel:
Exp(Y223)
= Exp(a + b × X223 – 2 × s)
= Exp(a + b × 322 – 2 × s)
= Exp(3.8078 + 0.0007 × 322 – 2 × 0.0482)
= Exp(3.9383)
= $51.33
April 15, 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(3.8078 + 0.0007 × 1,825 + 2 × 0.0482)
= Exp(5.1909)
= $179.63
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(3.8078 + 0.0007 × 1,825 – 2 × 0.0482)
= Exp(4.9980)
= $148.11
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 29.35% per annum.
- TJX price at the close of April 15, 2026 was $160.23 and was inside the primary price channel.
Secondary Trend
Start date: June 3, 2024
End date: April 15, 2026
a = 3.9669
b = 0.0006
s = 0.0377
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0006) – 1
= 24.48%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0377) – 1
= 16.27%
June 3, 2024 calculations
Top border of price channel:
Exp(Y787)
= Exp(a + b × X787 + 2 × s)
= Exp(a + b × 1,144 + 2 × s)
= Exp(3.9669 + 0.0006 × 1,144 + 2 × 0.0377)
= Exp(4.7284)
= $113.12
Bottom border of price channel:
Exp(Y787)
= Exp(a + b × X787 – 2 × s)
= Exp(a + b × 1,144 – 2 × s)
= Exp(3.9669 + 0.0006 × 1,144 – 2 × 0.0377)
= Exp(4.5777)
= $97.29
April 15, 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(3.9669 + 0.0006 × 1,825 + 2 × 0.0377)
= Exp(5.1369)
= $170.19
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(3.9669 + 0.0006 × 1,825 – 2 × 0.0377)
= Exp(4.9862)
= $146.38
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 24.48% per annum.
- TJX price at the close of April 15, 2026 was inside the secondary price channel.