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 125.08% per annum.
- DELL price at the close of April 2, 2025 was $95.33 and was lower than the bottom border of the primary price channel by $83.37 (46.65%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 21.00% per annum.
- DELL price at the close of April 2, 2025 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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 DELL 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 26, 2022
End date: July 26, 2024
a = 1.3854
b = 0.0022
s = 0.1281
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0022) – 1
= 125.08%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1281) – 1
= 66.91%
August 26, 2022 calculations
Top border of price channel:
Exp(Y604)
= Exp(a + b × X604 + 2 × s)
= Exp(a + b × 875 + 2 × s)
= Exp(1.3854 + 0.0022 × 875 + 2 × 0.1281)
= Exp(3.5864)
= $36.10
Bottom border of price channel:
Exp(Y604)
= Exp(a + b × X604 – 2 × s)
= Exp(a + b × 875 – 2 × s)
= Exp(1.3854 + 0.0022 × 875 – 2 × 0.1281)
= Exp(3.0741)
= $21.63
July 26, 2024 calculations
Top border of price channel:
Exp(Y1,084)
= Exp(a + b × X1,084 + 2 × s)
= Exp(a + b × 1,575 + 2 × s)
= Exp(1.3854 + 0.0022 × 1,575 + 2 × 0.1281)
= Exp(5.1423)
= $171.11
Bottom border of price channel:
Exp(Y1,084)
= Exp(a + b × X1,084 – 2 × s)
= Exp(a + b × 1,575 – 2 × s)
= Exp(1.3854 + 0.0022 × 1,575 – 2 × 0.1281)
= Exp(4.6300)
= $102.51
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 125.08% per annum.
- DELL price at the close of April 2, 2025 was $95.33 and was lower than the bottom border of the primary price channel by $83.37 (46.65%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: April 1, 2024
End date: April 2, 2025
a = 5.8358
b = -0.0006
s = 0.1079
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0006) – 1
= -21.00%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1079) – 1
= 53.97%
April 1, 2024 calculations
Top border of price channel:
Exp(Y1,003)
= Exp(a + b × X1,003 + 2 × s)
= Exp(a + b × 1,459 + 2 × s)
= Exp(5.8358 + -0.0006 × 1,459 + 2 × 0.1079)
= Exp(5.1092)
= $165.53
Bottom border of price channel:
Exp(Y1,003)
= Exp(a + b × X1,003 – 2 × s)
= Exp(a + b × 1,459 – 2 × s)
= Exp(5.8358 + -0.0006 × 1,459 – 2 × 0.1079)
= Exp(4.6776)
= $107.51
April 2, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(5.8358 + -0.0006 × 1,825 + 2 × 0.1079)
= Exp(4.8728)
= $130.68
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(5.8358 + -0.0006 × 1,825 – 2 × 0.1079)
= Exp(4.4412)
= $84.88
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 21.00% per annum.
- DELL price at the close of April 2, 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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