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 29.80% per annum.
- TJX price at the close of May 7, 2024 was $97.92 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 20.22% per annum.
- TJX price at the close of May 7, 2024 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 11, 2024
a = 3.3354
b = 0.0007
s = 0.0509
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 29.80%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0509) – 1
= 22.58%
March 4, 2022 calculations
Top border of price channel:
Exp(Y712)
= Exp(a + b × X712 + 2 × s)
= Exp(a + b × 1,031 + 2 × s)
= Exp(3.3354 + 0.0007 × 1,031 + 2 × 0.0509)
= Exp(4.1739)
= $64.97
Bottom border of price channel:
Exp(Y712)
= Exp(a + b × X712 – 2 × s)
= Exp(a + b × 1,031 – 2 × s)
= Exp(3.3354 + 0.0007 × 1,031 – 2 × 0.0509)
= Exp(3.9703)
= $53.00
April 11, 2024 calculations
Top border of price channel:
Exp(Y1,240)
= Exp(a + b × X1,240 + 2 × s)
= Exp(a + b × 1,800 + 2 × s)
= Exp(3.3354 + 0.0007 × 1,800 + 2 × 0.0509)
= Exp(4.7233)
= $112.54
Bottom border of price channel:
Exp(Y1,240)
= Exp(a + b × X1,240 – 2 × s)
= Exp(a + b × 1,800 – 2 × s)
= Exp(3.3354 + 0.0007 × 1,800 – 2 × 0.0509)
= Exp(4.5198)
= $91.81
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 29.80% per annum.
- TJX price at the close of May 7, 2024 was $97.92 and was inside the primary price channel.
Secondary Trend
Start date: November 10, 2022
End date: May 7, 2024
a = 3.6702
b = 0.0005
s = 0.0357
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0005) – 1
= 20.22%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0357) – 1
= 15.34%
November 10, 2022 calculations
Top border of price channel:
Exp(Y886)
= Exp(a + b × X886 + 2 × s)
= Exp(a + b × 1,282 + 2 × s)
= Exp(3.6702 + 0.0005 × 1,282 + 2 × 0.0357)
= Exp(4.3884)
= $80.51
Bottom border of price channel:
Exp(Y886)
= Exp(a + b × X886 – 2 × s)
= Exp(a + b × 1,282 – 2 × s)
= Exp(3.6702 + 0.0005 × 1,282 – 2 × 0.0357)
= Exp(4.2456)
= $69.80
May 7, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.6702 + 0.0005 × 1,826 + 2 × 0.0357)
= Exp(4.6628)
= $105.93
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.6702 + 0.0005 × 1,826 – 2 × 0.0357)
= Exp(4.5201)
= $91.84
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 20.22% per annum.
- TJX price at the close of May 7, 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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