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 71.60% per annum.
- CSCO price at the close of January 29, 2025 was $59.55 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 22.10% per annum.
- CSCO price at the close of January 29, 2025 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 CSCO 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: May 28, 2024
End date: January 24, 2025
a = 1.4327
b = 0.0015
s = 0.0295
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0015) – 1
= 71.60%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0295) – 1
= 12.54%
May 28, 2024 calculations
Top border of price channel:
Exp(Y1,088)
= Exp(a + b × X1,088 + 2 × s)
= Exp(a + b × 1,580 + 2 × s)
= Exp(1.4327 + 0.0015 × 1,580 + 2 × 0.0295)
= Exp(3.8293)
= $46.03
Bottom border of price channel:
Exp(Y1,088)
= Exp(a + b × X1,088 – 2 × s)
= Exp(a + b × 1,580 – 2 × s)
= Exp(1.4327 + 0.0015 × 1,580 – 2 × 0.0295)
= Exp(3.7112)
= $40.90
January 24, 2025 calculations
Top border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 + 2 × s)
= Exp(a + b × 1,821 + 2 × s)
= Exp(1.4327 + 0.0015 × 1,821 + 2 × 0.0295)
= Exp(4.1858)
= $65.75
Bottom border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 – 2 × s)
= Exp(a + b × 1,821 – 2 × s)
= Exp(1.4327 + 0.0015 × 1,821 – 2 × 0.0295)
= Exp(4.0677)
= $58.42
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 71.60% per annum.
- CSCO price at the close of January 29, 2025 was $59.55 and was inside the primary price channel.
Secondary Trend
Start date: November 6, 2024
End date: January 29, 2025
a = 3.0982
b = 0.0005
s = 0.0146
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0005) – 1
= 22.10%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0146) – 1
= 6.02%
November 6, 2024 calculations
Top border of price channel:
Exp(Y1,201)
= Exp(a + b × X1,201 + 2 × s)
= Exp(a + b × 1,742 + 2 × s)
= Exp(3.0982 + 0.0005 × 1,742 + 2 × 0.0146)
= Exp(4.0804)
= $59.17
Bottom border of price channel:
Exp(Y1,201)
= Exp(a + b × X1,201 – 2 × s)
= Exp(a + b × 1,742 – 2 × s)
= Exp(3.0982 + 0.0005 × 1,742 – 2 × 0.0146)
= Exp(4.0219)
= $55.81
January 29, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.0982 + 0.0005 × 1,826 + 2 × 0.0146)
= Exp(4.1263)
= $61.95
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.0982 + 0.0005 × 1,826 – 2 × 0.0146)
= Exp(4.0679)
= $58.43
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 22.10% per annum.
- CSCO price at the close of January 29, 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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