Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 14.66% per annum.
- CSCO price at the close of May 20, 2024 was $47.13 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 1.79% per annum.
- CSCO price at the close of May 20, 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 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: August 7, 2023
End date: May 20, 2024
a = 4.6485
b = -0.0004
s = 0.0306
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0004) – 1
= -14.66%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0306) – 1
= 13.02%
August 7, 2023 calculations
Top border of price channel:
Exp(Y1,060)
= Exp(a + b × X1,060 + 2 × s)
= Exp(a + b × 1,539 + 2 × s)
= Exp(4.6485 + -0.0004 × 1,539 + 2 × 0.0306)
= Exp(4.0412)
= $56.90
Bottom border of price channel:
Exp(Y1,060)
= Exp(a + b × X1,060 – 2 × s)
= Exp(a + b × 1,539 – 2 × s)
= Exp(4.6485 + -0.0004 × 1,539 – 2 × 0.0306)
= Exp(3.9189)
= $50.34
May 20, 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(4.6485 + -0.0004 × 1,826 + 2 × 0.0306)
= Exp(3.9166)
= $50.23
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.6485 + -0.0004 × 1,826 – 2 × 0.0306)
= Exp(3.7942)
= $44.44
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 14.66% per annum.
- CSCO price at the close of May 20, 2024 was $47.13 and was inside the primary price channel.
Secondary Trend
Start date: November 16, 2023
End date: May 20, 2024
a = 3.9738
b = 0.0000
s = 0.0234
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= -1.79%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0234) – 1
= 9.81%
November 16, 2023 calculations
Top border of price channel:
Exp(Y1,132)
= Exp(a + b × X1,132 + 2 × s)
= Exp(a + b × 1,640 + 2 × s)
= Exp(3.9738 + 0.0000 × 1,640 + 2 × 0.0234)
= Exp(3.9392)
= $51.38
Bottom border of price channel:
Exp(Y1,132)
= Exp(a + b × X1,132 – 2 × s)
= Exp(a + b × 1,640 – 2 × s)
= Exp(3.9738 + 0.0000 × 1,640 – 2 × 0.0234)
= Exp(3.8456)
= $46.79
May 20, 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(3.9738 + 0.0000 × 1,826 + 2 × 0.0234)
= Exp(3.9300)
= $50.91
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.9738 + 0.0000 × 1,826 – 2 × 0.0234)
= Exp(3.8364)
= $46.36
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 1.79% per annum.
- CSCO price at the close of May 20, 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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